Prefix Sums
Description
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.
Input
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.
Output
Print the minimum i such that Ai contains a number which is larger or equal than k.
Samples
2 2
1 1
1
3 6
1 1 1
2
3 1
1 0 1
0