First Prefix Average Above Threshold

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given n integers and integer threshold T, find the smallest one-based position i whose prefix average is strictly greater than T, or -1 if none exists.

Input

The first line contains n and T. The next line has exactly n integers in order.

Output

Print the first one-based position, or -1.

Subtasks

• Subtask 1 (20%): 1≤n≤10, |T|≤10, |a_i|≤10.
• Subtask 2 (30%): 1≤n≤1000, |T|≤1000, |a_i|≤1000.
• Subtask 3 (50%): 1≤n≤100000, |T|≤1000000, |a_i|≤10000.

Examples

Example 1

Input

4 3
1 2 9 0

Output

3

Explanation

Prefix sums are 1,3,12; the first average above three occurs at i=3.

Example 2

Input

3 5
5 5 5

Output

-1

Explanation

All prefix averages equal five, not strictly above it.