First Revenue Milestone

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given n nonnegative revenues in order, print the first number of rounds whose cumulative sum reaches T. T=0 yields zero; print -1 if the threshold is never reached.

Input

Integers n T, followed by exactly n nonnegative revenues.

Output

The first round count 0..n, or -1.

Subtasks

• Subtask 1 (20%): n ≤ 10, T ≤ 100, revenues 0..100.

• Subtask 2 (30%): n ≤ 1000, T ≤ 10^6, revenues 0..10^6.

• Subtask 3 (50%): n ≤ 100000, T ≤ 10^14, revenues 0..10^9.

Examples

Example 1

Input:

4 8
2 3 3 10

Output:

3

Explanation: Cumulative revenue first reaches eight at round three.

Example 2

Input:

2 0
0 0

Output:

0

Explanation: The zero threshold is met before any round.

Example 3

Input:

2 9
4 4

Output:

-1

Explanation: Total revenue eight is below nine.