Consider the function p(x), where x is an array of m integers, which returns an array y consisting of m+1 integers such that yi is equal to the sum of first i elements of array x (0≤i≤m).
You have an infinite sequence of arrays A0,A1,A2..., where A0 is given in the input, and for each i≥1 Ai=p(Ai-1). Also you have a positive integer k. You have to find minimum possible i such that Ai contains a number which is larger or equal than k.
The first line contains two integers n and k (2≤n≤200000, 1≤k≤1018). n is the size of array A0.
The second line contains n integers A00,A01... A0n-1 − the elements of A0 (0≤A0i≤109). At least two elements of A0 are positive.
Print the minimum i such that Ai contains a number which is larger or equal than k.
2 2
1 1
1
3 6
1 1 1
2
3 1
1 0 1
0