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Two sum

Easy
2000 ms limit256 MB memoryHash mapsArrays

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For each number, ask whether you have already seen the one it needs. A hash map answers that in constant time.

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Given an array of integers and a target value, return the indices of the two numbers that add up to the target.

Each input has exactly one solution, and you may not use the same element twice. Return the indices in increasing order.

Constraints#

  • 2 <= n <= 100000
  • -10^9 <= nums[i], target <= 10^9

Input

nums is a count then that many integers. target is one integer.

Output

Two space-separated indices, zero-based.

Examples

Input

4
2 7 11 15
9

Output

0 1

2 + 7 = 9, so the answer is the indices of those two values.

Input

3
3 2 4
6

Output

1 2

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