Two Sum

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

4 9
2 7 11 15

1 2

Example 2

5 6
3 2 4 8 10

2 3

Example 3

5 10
-1 4 9 11 2

1 4