You are given an array of integers and a target sum.

Find two distinct positions whose values add up to the target.

It is guaranteed that exactly one valid pair exists.

Input

The first line contains two integers ~n~ and ~target~, the size of the array and the target sum.

The second line contains ~n~ integers: ~a_1, a_2, \ldots, a_n~.

Output

Print two space-separated integers ~i~ and ~j~ (~i < j~), the 1-indexed positions of a pair such that ~a_i + a_j = target~.

Constraints

• ~2 \le n \le 2 \cdot 10^5~
• ~-10^9 \le a_i \le 10^9~
• ~-2 \cdot 10^9 \le target \le 2 \cdot 10^9~
• Exactly one valid pair exists.

Example 1

Input

4 9
2 7 11 15

Output

1 2

Example 2

Input

5 6
3 2 4 8 10

Output

2 3

Example 3

Input

5 10
-1 4 9 11 2

Output

1 4