TopCoder Statistics - Problem Statement

Problem Statement

You have a int[] A with N elements.

Your goal is to change it into a int[] that contains each number from 1 to N exactly once. The change will consist of zero or more steps. In each step, you may pick an arbitrary element of A and increment its value by k. You may pick the same element multiple times. Note that you are not allowed to decrement the value of any element.

You are given the int k and the int[] A. Return "POSSIBLE" if it is possible to achieve your goal. Return "IMPOSSIBLE" otherwise.

Definition

Class:: IncrementingSequence
Method:: canItBeDone
Parameters:: int, int[]
Returns:: String
Method signature:: String canItBeDone(int k, int[] A)
(be sure your method is public)

Notes

Return value is case-sensitive. For example, you can't return "Possible" or "possible" instead of "POSSIBLE".

Constraints

k will be between 1 and 10, inclusive.
A will contain between 1 and 50 elements, inclusive.
Each element of A will be between 1 and 50, inclusive.

Examples

3

{1,2,4,3}

Returns: "POSSIBLE"

This sequence of length 4 already contains all numbers from 1 to 4 exactly once. Note that their order does not matter.
5

{2,2}

Returns: "IMPOSSIBLE"
1

{1,1,1,1,1,1,1,1}

Returns: "POSSIBLE"

There are many ways to achieve the goal. For example, it is possible to obtain the sequence {1,2,3,4,5,6,7,8}. To do this, just increment the element at each position one by one until it reaches the required value.
2

{5,3,3,2,1}

Returns: "IMPOSSIBLE"

We want to have the values {1,2,3,4,5}, in any order. Currently, we are missing the 4. As k=2, the only way to produce a 4 is by incrementing a 2. But if we increment our only 2, we will have no way of producing another 2.
9

{1,2,3,1,4,5,6,7,9,8}

Returns: "POSSIBLE"
2

{1,1,1,1,1,1,2,2,2,2,2,2}

Returns: "POSSIBLE"
1

{1}

Returns: "POSSIBLE"
4

{13,16,9,41,3,24,25,21,12,34,22,39,31,33,10,35,27,1,6,8,44,29,15,5,45,14,40,28,20,26,36,43,7,11,38,19,4,37,46,32,23,18,2,17,30,42,47}

Returns: "POSSIBLE"
8

{1,13,12,36,29,20,15,10,1,35,17,15,26,11,13,4,3,5,15,39,28,21,16,18,8,22,2,33,27,19,14,7,18,38,32,24,17,30,6}

Returns: "POSSIBLE"
2

{1,21,2,23,11,13,28,24,27,7,8,22,33,19,12,26,27,16,16,31,17,34,32,10,6,7,13,23,30,20,2,3,14,3}

Returns: "POSSIBLE"
5

{9,32,18,5,22,33,13,17,2,26,24,35,14,15,23,3,29,20,16,27,18,11,10,8,1,7,4,34,36,19,21,30,6,12,31,25}

Returns: "POSSIBLE"
7

{22,27,39,34,36,43,25,16,24,2,33,8,18,37,42,15,13,48,30,17,33,29,4,39,37,32,23,28,31,11,3,40,45,14,19,1,6,19,20,7,21,41,5,35,10,12,2,17}

Returns: "POSSIBLE"
5

{2,4,2,1,5,3,1}

Returns: "POSSIBLE"
2

{2,26,8,20,23,4,27,12,9,1,4,5,16,25,19,31,14,28,22,13,21,24,17,23,8,18,28,1,7,15,11}

Returns: "POSSIBLE"
4

{14,5,13,4,3,22,12,6,10,8,9,11,17,19,3,9,2,15,18,20,19,4,1}

Returns: "POSSIBLE"
7

{31,1,16,20,7,36,46,10,41,23,42,8,5,9,34,32,14,11,6,35,25,45,50,47,18,40,28,12,30,39,27,3,24,37,44,38,4,15,10,29,26,43,19,48,6,33,21,49,2,22}

Returns: "POSSIBLE"
4

{1,2,4,3,1,2}

Returns: "POSSIBLE"
2

{6,11,2,20,13,14,6,21,7,1,4,12,5,3,9,8,19,17,15,14,18}

Returns: "POSSIBLE"
7

{6,7,8,3,1,9,3,2,4,5}

Returns: "POSSIBLE"
10

{8,30,8,17,35,3,12,21,24,34,10,9,36,38,1,10,6,3,39,30,27,1,26,19,22,29,7,37,25,14,13,5,2,28,15,4,33,31,16,22,41}

Returns: "POSSIBLE"
9

{1,8,2,2,3,5,4,9,3,4,1,6,7}

Returns: "POSSIBLE"
10

{2,16,9,21,10,15,12,13,14,9,22,3,17,27,18,3,11,1,8,10,14,28,25,26,19,5,4,6,7}

Returns: "POSSIBLE"
10

{3,2,17,16,15,7,19,23,8,24,1,10,8,5,9,15,22,12,11,6,13,14,21,26,20,4}

Returns: "POSSIBLE"
5

{21,13,24,22,18,26,3,25,33,2,6,6,31,14,4,7,1,10,29,2,5,20,4,32,8,27,31,25,28,17,15,35,34,9,16,23}

Returns: "POSSIBLE"
9

{2,1}

Returns: "POSSIBLE"
6

{20,11,36,44,9,12,39,1,25,43,29,33,16,50,3,40,14,42,43,13,18,27,38,32,2,47,31,5,15,4,10,6,35,19,7,39,48,28,17,21,23,46,22,34,37,26,12,41,8,30}

Returns: "POSSIBLE"
9

{3,2,1}

Returns: "POSSIBLE"
7

{1,2}

Returns: "POSSIBLE"
8

{2,10,18,6,12,8,11,7,13,5,19,12,17,9,3,13,14,4,16,15,1}

Returns: "POSSIBLE"
7

{4,5,7,2,3,1,6}

Returns: "POSSIBLE"
9

{6,4,7,5,1,2,3}

Returns: "POSSIBLE"
8

{9,10,14,24,23,21,12,6,15,26,12,3,8,25,16,19,27,5,4,10,2,5,22,1,7,17,11}

Returns: "POSSIBLE"
10

{11,19,26,6,7,9,15,12,27,22,5,23,6,14,20,1,8,10,11,20,24,7,25,2,3,29,3,4,8,28}

Returns: "POSSIBLE"
8

{28,10,21,18,1,12,2,31,3,14,27,4,6,25,5,22,7,39,20,5,17,30,38,24,15,34,33,19,8,40,26,29,27,9,15,36,24,8,11,33,29}

Returns: "POSSIBLE"
10

{28,8,33,1,32,26,10,12,9,4,36,5,16,20,37,35,3,34,5,24,18,31,13,29,2,21,1,7,13,14,6,27,19,17,22,25,30}

Returns: "POSSIBLE"
10

{3,14,39,12,18,19,25,2,42,22,4,23,24,13,9,12,29,38,31,1,11,31,33,16,10,18,8,20,15,26,5,11,40,7,30,37,35,27,16,17,6,4}

Returns: "POSSIBLE"
7

{35,7,2,16,23,26,13,24,37,30,1,33,17,29,8,15,20,12,28,10,38,14,6,5,18,27,32,3,13,40,25,4,39,15,31,4,19,9,21,36}

Returns: "POSSIBLE"
8

{5,7,6,3,8,4,2,2,1,1}

Returns: "POSSIBLE"
9

{6,1,4,5,3,2}

Returns: "POSSIBLE"
8

{9,20,19,24,7,25,5,4,14,21,15,16,6,1,15,8,1,10,13,22,18,18,3,4,2,3}

Returns: "POSSIBLE"
5

{17,1,10,13,7,23,14,11,5,22,1,20,2,10,1,3,12,16,18,9,3,4,4}

Returns: "POSSIBLE"
4

{3,15,2,12,8,3,6,1,13,1,4,14,8,7,1,2}

Returns: "POSSIBLE"
3

{41,32,24,16,34,34,2,6,27,7,42,40,8,11,11,19,1,43,22,35,18,23,13,9,21,20,38,33,29,15,31,36,17,10,5,26,12,3,30,4,28,25,39}

Returns: "POSSIBLE"
6

{2,4,5,1,1,6,3}

Returns: "POSSIBLE"
10

{34,26,10,23,2,3,13,31,11,12,15,8,30,7,9,11,29,6,7,1,27,15,20,5,14,9,26,33,8,22,22,16,4,28,24,35}

Returns: "POSSIBLE"
3

{7,11,18,10,2,9,18,2,8,16,12,20,1,4,3,6,10,15,8,22,14,13}

Returns: "POSSIBLE"
9

{8,1,3,4,7,2,9,6,5,1,2}

Returns: "POSSIBLE"
8

{35,11,2,7,34,5,25,3,21,14,27,8,13,20,24,21,4,18,25,22,1,15,18,6,30,31,1,32,10,7,9,12,28,3,36,16}

Returns: "POSSIBLE"
9

{2,3,1,4}

Returns: "POSSIBLE"
2

{48,7,29,24,41,40,50,7,44,11,34,13,23,39,27,37,45,14,33,22,3,36,32,30,6,31,3,8,28,4,20,35,17,49,6,42,1,12,38,25,24,18,16,19,46,47,2,21,43,15}

Returns: "POSSIBLE"
3

{13,16,41,3,38,24,8,37,7,25,20,9,18,23,26,40,30,32,19,3,31,32,21,1,15,28,36,6,22,39,4,14,28,2,10,5,27,17,5,26,33}

Returns: "POSSIBLE"
4

{2,3,4,1}

Returns: "POSSIBLE"
4

{6,30,9,36,1,19,32,23,10,15,34,26,16,16,8,11,31,5,33,24,2,28,27,7,31,37,3,18,9,4,21,25,17,22,14,8,29}

Returns: "POSSIBLE"
2

{28,14,32,8,17,3,15,26,13,7,4,19,27,29,38,16,21,20,23,34,5,2,31,30,37,10,42,35,1,18,22,11,36,24,39,25,33,12,6,40,9,41}

Returns: "POSSIBLE"
3

{1,3,14,11,9,4,8,7,6,7,2,7,5,9}

Returns: "POSSIBLE"
6

{5,11,9,18,13,8,12,16,8,10,17,6,4,7,2,1,3,9}

Returns: "POSSIBLE"
7

{22,8,2,11,1,1,5,7,13,7,3,2,4,10,12,20,9,14,19,3,4,6}

Returns: "POSSIBLE"
9

{4,7,5,1,4,9,2,6,5,1,6,4,3,6,5,2,5,5,2,1,9,8,7,7,7,8,6,4,2,4,3,8,3,1,2,1,9,3,6,9,3,7,8}

Returns: "POSSIBLE"
7

{5,4,6,3,3,1,3,5,5,4,2,2,4,1,7,2,1,7,3,7,1,3,3,6,2,6,4,2,1,4,6,6,6,1,2,5,5,7,7,5,4}

Returns: "POSSIBLE"
7

{3,4,1,7,3,3,5,2,6,6,5,5,6,7,6,2,2,23,6,7,1,4,28,2,1,4,4,5,1,5,1,4,1,3,10,4,2,7,6,7,5,10,15,2}

Returns: "POSSIBLE"
10

{1,1,4,5,9,2,10,7,5,4,8,10,2,10,5,8,6,4,9,7,10,3,4,4,3,2,2,1,1,6,7,1,3,3,8,7,5,6,9,6,2,3,9,8}

Returns: "POSSIBLE"
10

{1,2,1,9,5,6,2,1,3,1,10,8,9,3,7,2,4,9,5,5,2,10,6,10,4,10,6,7,4,1,8,9,8,3,3,5,7,8,4,6,7}

Returns: "POSSIBLE"
6

{5,4,1,2,5,4,5,3,6,4,6,4,3,5,6,4,3,2,6,3,1,2,1,5,4,6,2,2,4,1,1,2,6,1,2,4,1,3,2,3,1,6,5,3,6,1,5,2,5,3}

Returns: "POSSIBLE"
9

{3,1,2,9,8,5,1,1,3,5,9,8,2,2,9,6,1,6,7,6,4,2,9,3,7,7,8,7,2,1,5,9,4,7,4,4,4,1,2,8,8,5,6,5,6,3,3}

Returns: "POSSIBLE"
7

{3,2,6,5,2,4,4,1,7,1,6,4,3,7,1,7,2,3,7,1,7,4,1,3,2,1,1,3,5,4,3,6,6,7,6,2,3,5,2,5,4,2,4,5,6,5}

Returns: "POSSIBLE"
8

{6,3,6,3,8,8,7,4,1,6,1,4,1,5,5,5,2,3,7,3,3,4,5,6,5,8,8,4,1,1,7,1,2,2,2,7,3,2,4,6,2,4,8,7}

Returns: "POSSIBLE"
10

{3,6,7,1,5,6,1,1,10,5,3,1,7,6,8,10,8,2,10,10,5,4,9,7,7,2,8,1,4,6,8,2,3,2,3,4,9,9,3,2,9,4,5}

Returns: "POSSIBLE"
6

{12,25,22,27,5,15,31,26,1,20,8,3,14,11,23,29,34,32,5,21,16,2,10,6,7,13,33,18,28,17,24,9,30,19}

Returns: "IMPOSSIBLE"
2

{2,11,11,17,14,5,8,9,4,8,16,7,7,12,15,1,1}

Returns: "IMPOSSIBLE"
8

{17,11,6,23,14,13,18,10,22,13,4,1,2,8,5,7,15,19,16,13,3,9,20}

Returns: "IMPOSSIBLE"
5

{20,13,2,5,13,6,3,4,1,2,18,4,15,19,6,9,8,12,5,16}

Returns: "IMPOSSIBLE"
5

{3,14,22,2,18,6,4,17,6,9,13,2,11,7,21,4,5,1,3,11,5,23,20}

Returns: "IMPOSSIBLE"
2

{17,15,9,22,13,23,21,17,12,5,14,2,11,4,6,19,1,10,7,18,20,8,1}

Returns: "IMPOSSIBLE"
4

{1,10,10,12,32,21,17,20,28,26,27,6,24,23,33,19,18,15,25,2,7,16,8,30,11,13,29,14,3,4,22,31,5}

Returns: "IMPOSSIBLE"
8

{16,6,7,1,19,21,9,20,18,30,24,15,31,5,28,26,17,10,27,8,6,15,25,3,14,2,11,4,13,13,5}

Returns: "IMPOSSIBLE"
8

{2,2}

Returns: "IMPOSSIBLE"
8

{19,29,31,34,18,30,3,21,3,9,33,24,24,41,14,4,26,28,10,35,30,15,17,23,5,17,7,13,16,28,37,4,20,40,8,1,2,11,6,39,23}

Returns: "IMPOSSIBLE"
9

{7,1,6,5,4,8,2,1,9,4,6,2,4,3,5,7}

Returns: "IMPOSSIBLE"
9

{16,15,11,2,14,7,9,3,3,5,2,4,17,13,6,8,10}

Returns: "IMPOSSIBLE"
3

{13,2,11,9,18,6,19,12,15,4,4,15,3,20,5,5,14,10,13,1}

Returns: "IMPOSSIBLE"
9

{4,1,6,4,5,2}

Returns: "IMPOSSIBLE"
10

{27,13,7,4,2,8,10,24,25,18,23,12,9,6,1,14,10,5,15,2,27,19,11,16,3,17,21}

Returns: "IMPOSSIBLE"
4

{3,6,3,11,22,25,28,4,18,8,27,19,30,10,21,27,34,20,23,24,17,15,12,2,36,5,1,31,29,13,33,10,5,31,8,24}

Returns: "IMPOSSIBLE"
8

{8,27,36,3,38,42,37,40,30,22,23,6,31,26,43,39,24,2,7,18,13,14,5,16,24,20,41,46,3,45,15,28,9,35,41,33,2,34,14,40,4,47,29,1,4,19,44,17,25}

Returns: "IMPOSSIBLE"
9

{14,6,1,3,5,12,16,10,8,9,7,2,4,13,15,12}

Returns: "IMPOSSIBLE"
3

{36,15,2,24,22,29,26,37,16,31,19,12,20,40,42,43,7,21,4,1,33,6,9,3,44,32,34,11,27,41,17,10,25,23,15,12,39,30,35,5,38,42,5,28,13}

Returns: "IMPOSSIBLE"
9

{6,2,3,8,7,5,2,1,4,9}

Returns: "IMPOSSIBLE"
5

{12,41,31,23,24,8,36,32,15,5,2,17,26,27,30,30,4,4,13,32,33,25,43,7,29,1,22,14,5,15,11,44,13,1,39,21,42,9,16,28,35,19,23,34}

Returns: "IMPOSSIBLE"
4

{15,6,2,2,4,3,5,14,4,7,12,9,7,12,2,9}

Returns: "IMPOSSIBLE"
2

{11,8,3,7,1,6,20,16,17,4,11,21,9,14,12,22,2,13,19,18,5,15}

Returns: "IMPOSSIBLE"
6

{21,22,19,5,24,26,23,2,11,4,6,14,25,10,20,1,7,11,6,4,2,18,16,9,13,15}

Returns: "IMPOSSIBLE"
10

{7,1,10,15,9,6,3,12,5,11,4,2,13,8,5}

Returns: "IMPOSSIBLE"
10

{5,6,2,17,14,1,8,13,22,12,36,27,8,35,26,20,3,31,24,11,6,28,9,10,15,30,16,21,29,23,19,33,32,4,7,34,37}

Returns: "IMPOSSIBLE"
7

{3,7,18,27,4,17,28,25,9,13,6,15,10,23,11,10,21,7,29,22,8,2,30,5,5,1,12,26,20,24}

Returns: "IMPOSSIBLE"
6

{16,37,12,39,42,23,3,29,13,10,21,12,28,26,1,11,15,5,38,8,4,43,33,9,32,6,20,25,22,30,36,35,14,1,23,38,40,7,35,11,24,2,27,25}

Returns: "IMPOSSIBLE"
2

{17,38,35,28,24,37,3,40,44,41,29,15,1,23,37,11,33,7,9,4,25,34,10,19,14,27,8,21,45,12,31,39,26,5,30,2,13,32,43,6,16,20,49,42,47,46,48,22,18}

Returns: "IMPOSSIBLE"
8

{1,5,7,2,2,5,8,6,3,3,1}

Returns: "IMPOSSIBLE"
7

{2,1,7,5,6,5,3}

Returns: "IMPOSSIBLE"
9

{3,3,11,9,20,23,4,2,13,18,27,16,19,6,21,14,25,10,23,8,7,5,24,15,1,17,26}

Returns: "IMPOSSIBLE"
4

{4,2,4,1,11,4,7,1,9,3,7,6,1}

Returns: "IMPOSSIBLE"
7

{43,6,31,27,10,7,30,20,8,23,23,2,13,35,33,3,14,30,4,25,19,39,42,9,11,27,12,24,21,29,15,26,41,40,36,1,18,5,17,31,28,32,9}

Returns: "IMPOSSIBLE"
3

{8,33,32,13,12,28,37,24,7,40,3,22,39,29,35,6,20,36,10,17,14,38,4,16,31,23,1,2,16,5,27,21,18,30,11,34,9,25,23,19}

Returns: "IMPOSSIBLE"
8

{27,3,19,20,10,8,24,10,2,5,3,7,17,29,13,22,17,12,6,9,6,1,26,8,12,24,22,7,21,4}

Returns: "IMPOSSIBLE"
9

{46,24,8,23,29,47,26,42,40,36,20,32,37,25,7,21,16,10,22,4,14,17,19,38,39,44,9,2,35,11,6,13,3,45,12,30,5,49,33,31,15,43,27,48,41,28,50,35,1,18}

Returns: "IMPOSSIBLE"
6

{8,23,13,4,9,7,5,5,14,18,11,14,15,19,6,3,22,1,12,22,10,2,10}

Returns: "IMPOSSIBLE"
3

{1,30,11,28,24,32,31,21,36,37,15,2,12,6,22,2,10,18,20,7,17,8,3,5,34,39,38,35,23,20,29,33,19,25,16,13,14,24,9}

Returns: "IMPOSSIBLE"
4

{1,2,3,1,5,2}

Returns: "IMPOSSIBLE"
10

{3,2,2}

Returns: "IMPOSSIBLE"
10

{5,9,5,7,11,3,5,6,3,8,2,17,6,14,10,10,9,18,1,2}

Returns: "IMPOSSIBLE"
10

{1,3,16,12,21,10,8,9,19,5,2,24,22,10,17,5,4,7,24,8,1,6,14,13}

Returns: "IMPOSSIBLE"
8

{7,5,2,5,3,6,1,8}

Returns: "IMPOSSIBLE"
6

{4,2,3,2}

Returns: "IMPOSSIBLE"
6

{8,21,10,2,7,13,12,17,14,9,6,15,4,11,1,3,21,5,16,12,19}

Returns: "IMPOSSIBLE"
2

{2,2}

Returns: "IMPOSSIBLE"
9

{8,5,26,14,10,3,4,7,10,25,15,20,20,13,23,27,18,9,1,6,16,24,3,12,2,14,17,28,11}

Returns: "IMPOSSIBLE"
7

{4,5,1,4,2,6,7,3,3,2,1,6}

Returns: "IMPOSSIBLE"
4

{3,1,2,2,4}

Returns: "IMPOSSIBLE"
6

{34,2,17,31,13,10,3,7,16,33,23,8,18,7,22,13,30,9,21,26,2,12,30,6,2,22,4,31,19,33,35,13,5,18,27}

Returns: "IMPOSSIBLE"
2

{5,5,5,5,5}

Returns: "IMPOSSIBLE"
7

{28,42,4,12,39,2,21,13,11,35,44,5,37,4,33,24,32,4,30,9,21,9,41,42,25,22,22,18,17,16,35,43,10,26,8,12,30,28,21,41,24,37,35,14}

Returns: "IMPOSSIBLE"
9

{16,22,28,25,9,30,16,10,10,28,21,10,6,24,16,28,10,23,27,19,4,30,30,11,27,5,16,10,25,8}

Returns: "IMPOSSIBLE"
4

{29,8,12,31,15,15,17,3,8,21,5,21,30,14,6,29,3,18,13,28,18,26,5,5,20,22,24,1,8,25,24}

Returns: "IMPOSSIBLE"
2

{9,12,21,5,14,3,21,4,8,11,9,5,8,18,11,16,17,16,21,15,10}

Returns: "IMPOSSIBLE"
6

{35,7,10,41,11,30,22,3,40,25,31,2,41,13,10,18,21,15,24,23,20,41,32,36,26,7,41,19,41,19,32,4,26,11,26,20,13,30,8,30,38}

Returns: "IMPOSSIBLE"
2

{2,2}

Returns: "IMPOSSIBLE"
3

{6,17,2,4,3,13,17,8,9,17,10,11,3,17,17,15,9}

Returns: "IMPOSSIBLE"
10

{38,37,33,37,29,26,28,6,10,42,10,15,10,5,33,12,32,22,6,5,42,17,30,32,33,40,20,24,27,15,22,41,19,10,19,4,32,37,23,15,42,11}

Returns: "IMPOSSIBLE"
10

{14,10,14,15,16,4,5,10,9,11,17,10,12,8,7,10,8}

Returns: "IMPOSSIBLE"
2

{12,12,12,12,12,12,12,12,12,12,12,12}

Returns: "IMPOSSIBLE"
10

{3,10,6,12,21,19,2,11,16,13,4,6,27,13,8,28,14,17,22,6,7,20,17,2,25,11,25,2}

Returns: "IMPOSSIBLE"
9

{33,13,18,20,17,14,23,20,31,33,7,24,8,9,15,17,2,11,16,3,27,29,7,21,11,12,13,32,32,19,16,9,5}

Returns: "IMPOSSIBLE"
9

{33,28,5,13,34,11,41,40,5,13,31,35,22,43,26,32,11,28,17,24,39,19,32,7,40,43,43,26,10,33,3,16,22,28,8,14,23,21,12,19,5,29,14}

Returns: "IMPOSSIBLE"
3

{9,19,40,18,11,37,21,39,13,33,50,50,24,3,46,27,27,31,46,38,15,43,49,5,44,27,45,8,39,6,12,13,35,21,37,9,30,34,33,5,5,17,12,43,25,24,30,48,9,19}

Returns: "IMPOSSIBLE"
9

{7,7,7,7,7,7,7}

Returns: "IMPOSSIBLE"
8

{29,30,10,15,4,28,18,7,30,7,13,3,13,19,15,5,21,13,20,3,14,9,20,23,30,13,10,9,5,25}

Returns: "IMPOSSIBLE"
10

{47,3,19,6,34,7,20,34,21,15,24,21,5,7,48,23,39,46,2,10,28,18,35,4,32,26,11,45,17,30,41,4,12,38,42,36,8,25,31,27,1,34,12,28,19,43,9,13}

Returns: "IMPOSSIBLE"
6

{17,4,16,9,14,5,17,14,12,2,2,11,10,17,11,17,6}

Returns: "IMPOSSIBLE"
3

{13,18,18,18,11,13,15,9,18,18,9,13,16,13,11,18,18,15}

Returns: "IMPOSSIBLE"
7

{12,37,19,25,34,22,40,17,18,6,39,13,30,34,36,39,30,10,3,15,43,22,44,41,4,21,10,28,26,10,7,36,44,25,16,31,32,12,9,45,29,24,3,18,4}

Returns: "IMPOSSIBLE"
6

{28,33,8,25,24,27,28,15,24,25,5,33,12,3,21,13,38,30,9,34,24,6,3,5,20,2,4,25,10,11,35,5,18,2,24,8,37,19}

Returns: "IMPOSSIBLE"
7

{6,11,22,37,16,32,3,7,32,21,4,6,13,23,9,29,3,37,8,23,15,35,21,20,18,24,11,13,7,31,29,27,36,38,25,31,14,32}

Returns: "IMPOSSIBLE"
8

{11,12,15,21,13,5,10,6,12,9,7,4,19,12,6,6,9,8,6,7,17}

Returns: "IMPOSSIBLE"
2

{37,8,33,27,5,21,23,29,38,10,20,15,21,40,24,30,12,24,18,35,4,33,30,39,17,29,16,27,19,1,12,4,40,9,21,9,31,8,35,37}

Returns: "IMPOSSIBLE"
8

{6,10,13,35,3,32,4,21,26,36,38,15,26,22,8,2,3,1,34,29,17,22,1,16,15,7,34,13,17,20,3,19,31,30,20,5,28,24}

Returns: "IMPOSSIBLE"
3

{14,3,14,14,8,10,10,10,11,14,14,9,13,13}

Returns: "IMPOSSIBLE"
5

{8,32,12,17,30,33,3,20,11,16,29,10,33,19,20,27,12,28,23,9,4,26,16,3,21,3,27,6,7,31,12,19,33}

Returns: "IMPOSSIBLE"
6

{4,4,4,4}

Returns: "IMPOSSIBLE"
3

{8,7,8,8,6,7,6,6}

Returns: "IMPOSSIBLE"
10

{18,5,34,7,38,24,4,20,36,13,40,27,33,2,33,10,15,22,23,22,30,7,12,26,15,38,40,9,18,23,28,13,36,18,40,15,29,10,40,27}

Returns: "IMPOSSIBLE"
6

{2,2}

Returns: "IMPOSSIBLE"
10

{11,4,5,6,11,12,5,6,8,5,12,11}

Returns: "IMPOSSIBLE"
10

{5,6,9,22,12,14,14,9,22,16,22,8,5,10,16,7,9,14,14,22,5,19}

Returns: "IMPOSSIBLE"
7

{8,5,4,6,2,6,13,1,9,3,2,12,13,4,7,14,11,3}

Returns: "IMPOSSIBLE"
8

{31,12,8,15,6,28,26,28,13,22,9,18,11,25,24,30,2,21,24,1,18,20,4,19,31,16,14,5,26,6,3}

Returns: "IMPOSSIBLE"
3

{3,3,3}

Returns: "IMPOSSIBLE"
8

{5,5,5,5,5}

Returns: "IMPOSSIBLE"
2

{6,13,2,4,22,3,20,2,16,8,6,15,14,2,9,5,21,12,17,18,9,17,20}

Returns: "IMPOSSIBLE"
2

{9,9,9,9,9,9,9,9,9}

Returns: "IMPOSSIBLE"
10

{11,12,9,6,4,4,6,9,7,12,12,5}

Returns: "IMPOSSIBLE"
9

{28,32,9,5,36,29,34,23,12,30,19,4,21,43,14,25,10,36,10,34,2,16,43,15,31,39,22,50,26,17,6,50,8,5,18,47,12,39,40,47,20,37,16,46,9,27,41,28,15,1}

Returns: "IMPOSSIBLE"
10

{17,17,22,15,18,31,36,6,39,38,35,29,2,18,28,13,26,17,22,9,12,7,4,30,41,1,40,33,25,16,38,24,12,10,26,41,2,32,6,43,11,10,33}

Returns: "IMPOSSIBLE"
4

{1,1,1,1,1,1,1,1,1,1}

Returns: "IMPOSSIBLE"
2

{1,1,1,1}

Returns: "IMPOSSIBLE"
5

{22,6,12,33,2,45,33,13,30,35,28,41,39,37,34,11,10,21,4,44,17,23,42,41,40,14,24,16,14,5,27,8,31,16,26,7,32,38,1,10,19,20,35,25,7}

Returns: "IMPOSSIBLE"
8

{7,38,2,42,17,39,27,36,5,43,14,15,22,13,34,32,44,32,27,16,34,1,45,41,3,19,22,37,47,29,10,47,20,9,28,43,25,11,26,23,9,13,12,4,8,25,23}

Returns: "IMPOSSIBLE"
8

{42,41,4,29,46,10,36,46,43,41,15,11,24,34,23,26,38,3,7,15,5,12,31,2,34,28,24,23,19,35,30,37,33,14,10,20,17,5,8,40,45,2,48,26,6,8,22,8}

Returns: "IMPOSSIBLE"
2

{1,1}

Returns: "IMPOSSIBLE"
7

{25,37,17,26,18,14,3,8,4,50,1,49,31,42,15,38,3,17,5,20,6,32,14,19,24,8,34,43,37,6,36,6,45,32,2,8,47,31,29,24,18,48,40,18,41,44,14,33,27,42}

Returns: "IMPOSSIBLE"
4

{3,11,12,11,4,6,5,5,4,6,5,12}

Returns: "IMPOSSIBLE"
8

{1,1}

Returns: "IMPOSSIBLE"
2

{16,31,34,28,25,4,23,11,20,2,7,25,24,18,11,3,6,33,34,16,13,15,32,24,18,9,8,29,10,2,14,18,29,21}

Returns: "IMPOSSIBLE"
4

{2,5,5,2,4}

Returns: "IMPOSSIBLE"
9

{9,26,1,19,4,4,20,18,26,3,14,13,11,22,6,22,2,15,35,7,23,1,32,7,19,29,19,15,36,16,28,4,18,23,23,9,21}

Returns: "IMPOSSIBLE"
8

{5,26,5,3,17,13,25,14,2,3,19,5,7,20,3,6,8,24,15,1,25,18,3,25,3,23,23}

Returns: "IMPOSSIBLE"
6

{32,34,44,27,25,34,33,19,40,27,7,41,37,25,35,14,5,10,40,3,16,9,31,29,23,3,27,19,13,17,22,12,42,1,36,10,46,25,47,5,23,43,46,21,20,16,7,2}

Returns: "IMPOSSIBLE"
5

{9,22,11,15,14,17,26,16,14,6,20,18,8,18,8,26,18,22,3,5,10,1,5,6,2,17}

Returns: "IMPOSSIBLE"
6

{5,5,5,4,4,6}

Returns: "IMPOSSIBLE"
5

{1,2,13,7,6,27,8,16,19,8,9,17,28,3,35,24,30,25,36,17,37,21,21,21,20,28,14,22,19,29,32,11,1,5,10,32,4}

Returns: "IMPOSSIBLE"
6

{3,2,2,8,7,5,3,8,9,3}

Returns: "IMPOSSIBLE"
4

{31,27,9,29,13,11,21,20,32,15,6,8,21,28,8,2,23,30,10,1,20,32,13,2,9,6,23,19,19,3,14,22}

Returns: "IMPOSSIBLE"
10

{4,1,1,2,17,6,2,5,4,8,5,7,7,3,8,9,7,1}

Returns: "IMPOSSIBLE"
2

{22,13,19,7,2,16,16,1,10,6,10,24,15,21,4,18,10,3,11,5,20,25,5,13,25}

Returns: "IMPOSSIBLE"
6

{29,27,23,14,30,9,18,2,19,4,2,29,13,13,27,2,5,16,33,24,15,4,29,3,33,10,13,1,12,20,5,20,8,20}

Returns: "IMPOSSIBLE"
5

{20,50,32,10,25,24,41,29,44,44,16,26,34,36,27,29,15,5,5,1,23,38,12,21,10,35,48,34,20,21,40,7,33,43,3,17,30,13,19,15,13,8,43,32,9,44,48,48,39,2}

Returns: "IMPOSSIBLE"
8

{25,6,11,13,24,13,10,30,8,21,19,1,16,30,18,7,20,4,15,1,2,6,11,21,28,29,26,19,26,5,15}

Returns: "IMPOSSIBLE"
6

{1,1}

Returns: "IMPOSSIBLE"
9

{4,10,20,23,8,13,14,25,32,25,7,22,18,37,18,13,11,5,29,12,2,9,8,12,5,34,15,14,34,1,35,24,35,17,8,1,9}

Returns: "IMPOSSIBLE"
3

{17,5,41,31,11,44,38,26,32,24,25,10,14,48,5,43,36,49,47,4,31,14,49,8,31,8,19,3,4,28,36,29,19,22,42,37,13,2,24,2,14,41,27,47,31,8,40,17,27,12}

Returns: "IMPOSSIBLE"
9

{18,5,43,15,37,1,3,23,18,3,31,34,12,28,26,10,3,42,24,25,14,26,16,42,37,31,21,1,15,38,26,39,41,29,43,22,9,32,29,3,38,8,9,20,6}

Returns: "IMPOSSIBLE"
9

{4,3,3,4}

Returns: "IMPOSSIBLE"
3

{1,1,1,1}

Returns: "IMPOSSIBLE"
9

{5,6,2,6,6,4}

Returns: "IMPOSSIBLE"
8

{27,1,5,13,16,35,2,20,11,18,3,4,6,3,20,25,23,17,14,11,29,34,7,36,25,19,31,15,28,9,23,17,9,33,16,26}

Returns: "IMPOSSIBLE"
8

{7,3,29,1,26,40,7,22,23,4,4,13,25,35,28,33,27,15,24,8,36,6,11,23,5,38,18,3,31,25,12,16,30,12,23,6,9,19,20,33}

Returns: "IMPOSSIBLE"
5

{30,24,46,3,28,1,27,41,20,40,20,13,42,24,36,22,40,46,13,5,13,38,19,5,34,41,29,10,28,18,17,35,38,9,15,6,45,2,16,31,32,16,9,7,36,24}

Returns: "IMPOSSIBLE"
3

{15,3,10,1,12,7,14,13,3,14,6,4,8,1,7,10,1}

Returns: "IMPOSSIBLE"
4

{26,9,25,17,23,12,3,18,1,4,6,4,10,3,12,14,22,20,7,19,7,15,19,20,8,1}

Returns: "IMPOSSIBLE"
4

{13,2,12,21,24,7,22,21,7,1,12,4,16,10,20,23,10,19,16,9,4,13,2,9,5}

Returns: "IMPOSSIBLE"
3

{29,8,18,6,31,29,14,10,20,27,9,18,25,15,30,13,23,22,2,4,12,22,29,16,5,19,10,1,21,3,26,6}

Returns: "IMPOSSIBLE"
3

{2,3,4,5,6,7,8,9,10}

Returns: "IMPOSSIBLE"
10

{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30}

Returns: "POSSIBLE"
10

{11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,11,12,13,14,5,6,7,8,9,10}

Returns: "IMPOSSIBLE"
8

{7,6,1,2,4,5,3,8}

Returns: "POSSIBLE"
3

{5,7,33,2,35,1,39,11,43,44,36,15,40,30,29,9,15,13,26,6,11,23,37,32,19,4,28,21,38,17,5,13,26,25,33,7,34,3,27,20,18,31,7,21}

Returns: "IMPOSSIBLE"
10

{1,2}

Returns: "POSSIBLE"
6

{6,5,3,5,7,8,12,3,2,5,16,3,1,3,6,1,4,4,1,8,2}

Returns: "POSSIBLE"
2

{24,29,1,11,42,43,44,9,1,2,33,30,41,11,27,32,14,33,8,17,36,40,20,22,10,27,15,17,16,44,35,41,18,32,27,6,17,26,32,10,5,19,4,35}

Returns: "IMPOSSIBLE"
2

{17,2,24,5,5,26,20,31,23,18,29,8,23,16,29,11,22,2,5,32,17,28,32,11,8,7,10,10,21,2,11,15}

Returns: "IMPOSSIBLE"
8

{4,1,2,3,5}

Returns: "POSSIBLE"
4

{18,29,37,4,19,32,27,23,38,15,25,14,8,10,13,7,35,9,10,31,12,2,5,22,30,44,1,16,16,28,33,41,3,24,34,42,39,21,40,17,32,26,15,39}

Returns: "IMPOSSIBLE"
8

{4,8,2,12,1,8,1,6,3,7,2,18,5,3,7,11,14,1,5}

Returns: "POSSIBLE"
3

{15,7,28,21,22,3,33,39,31,1,26,20,34,36,19,20,9,9,32,15,4,4,2,38,7,22,14,11,13,21,27,25,5,27,35,29,24,5,8}

Returns: "IMPOSSIBLE"
5

{2, 2 }

Returns: "IMPOSSIBLE"
1

{1 }

Returns: "POSSIBLE"
10

{1, 1, 4 }

Returns: "IMPOSSIBLE"
2

{5, 3, 3, 2, 1 }

Returns: "IMPOSSIBLE"
1

{3, 2, 1 }

Returns: "POSSIBLE"
1

{1, 2, 5 }

Returns: "IMPOSSIBLE"
1

{2 }

Returns: "IMPOSSIBLE"
9

{1, 2, 3, 1, 4, 5, 6, 7, 9, 8 }

Returns: "POSSIBLE"
9

{1, 1, 1, 1, 1, 1, 1, 1, 1 }

Returns: "IMPOSSIBLE"
2

{1, 4 }

Returns: "IMPOSSIBLE"
4

{3 }

Returns: "IMPOSSIBLE"
2

{2, 3, 4, 5 }

Returns: "IMPOSSIBLE"
1

{3, 3, 3, 3 }

Returns: "IMPOSSIBLE"
1

{3, 3, 3 }

Returns: "IMPOSSIBLE"
2

{2 }

Returns: "IMPOSSIBLE"
1

{1, 1, 1, 1, 1, 1, 1, 1 }

Returns: "POSSIBLE"
5

{5, 5, 5, 5, 5 }

Returns: "IMPOSSIBLE"
4

{1, 1, 1, 3 }

Returns: "IMPOSSIBLE"
2

{1, 2, 2, 3 }

Returns: "POSSIBLE"
1

{50 }

Returns: "IMPOSSIBLE"
6

{1, 2, 4, 3 }

Returns: "POSSIBLE"
5

{1, 1, 2, 3, 4, 5, 6, 7, 8, 9 }

Returns: "IMPOSSIBLE"
3

{1, 2, 2, 2 }

Returns: "IMPOSSIBLE"
2

{1, 1, 4 }

Returns: "IMPOSSIBLE"
7

{1, 9 }

Returns: "IMPOSSIBLE"
1

{1, 1, 1, 1, 2, 3, 4 }

Returns: "POSSIBLE"
2

{1, 1, 1, 1, 1, 1, 1, 1, 2 }

Returns: "IMPOSSIBLE"
2

{1, 2, 2, 2 }

Returns: "IMPOSSIBLE"
10

{5 }

Returns: "IMPOSSIBLE"
1

{2, 2 }

Returns: "IMPOSSIBLE"
2

{1, 2, 3, 4, 6, 1 }

Returns: "POSSIBLE"
2

{1, 2, 3, 3, 4, 4 }

Returns: "POSSIBLE"
2

{1, 1, 1, 1 }

Returns: "IMPOSSIBLE"
1

{1, 1, 1, 5 }

Returns: "IMPOSSIBLE"
4

{2, 3, 4, 5 }

Returns: "IMPOSSIBLE"
2

{1, 2, 3, 13 }

Returns: "IMPOSSIBLE"
5

{6 }

Returns: "IMPOSSIBLE"
3

{1, 2, 2, 2, 2, 3 }

Returns: "IMPOSSIBLE"
1

{1, 1, 3, 5 }

Returns: "IMPOSSIBLE"
2

{1, 3, 3, 3 }

Returns: "IMPOSSIBLE"
2

{1, 2, 3, 3, 4, 5, 5, 6, 8 }

Returns: "POSSIBLE"
4

{1, 1, 1, 1, 1, 1, 1, 1 }

Returns: "IMPOSSIBLE"
1

{2, 2, 3, 4 }

Returns: "IMPOSSIBLE"

Statistics

Problem Statement for "IncrementingSequence"

Problem Statement

Definition

Notes

Constraints

Examples