Two Sum

Given a list of integers and a target value, find the two indices whose values add up to the target.

You may assume there is exactly one valid pair, and you cannot use the same element twice. Print the indices in ascending order.

Input

• Line 1: n integers separated by spaces (the list), with 2 <= n <= 2·10^4 and each value between -10^9 and 10^9.
• Line 2: a single integer target (-2·10^9 <= target <= 2·10^9).

Output

Two 0-based indices i j (with i < j) such that nums[i] + nums[j] == target.

Examples

Input:
2 7 11 15
9

Output:
0 1

Input:
3 2 4
6

Output:
1 2

Input:
3 3
6

Output:
0 1

The same value can appear twice. As long as they are at different indices, they still count as two separate numbers.

Input:
-3 4 3 90
0

Output:
0 2

Negative numbers work the same way: -3 + 3 == 0.