Given an array $A$ of $n$ integers. Find 3 different indices $i, j, k$ that $A_i + A_j + A_K$ = $x$.

Input

• The first line contains 2 integers $n, x$.
• The second line contains $n$ integers $A_i$.

Output

• Print $i, j, k$. If there are multiple answer, print any of them. It is guaranteed that at least 1 answer exists.

Constraints

• $1 \le n \le 5000$.
• $1 \le A_i, x \le 10^9$

Example

Input:

4 8
1 2 5 7

Output:

1 2 3