The Great Treasure Hunt

In the bustling city of Numeropolis, Detective Sum is on a mission to catch a pair of cunning thieves. The thieves have stolen a precious artifact worth exactly X gold coins.

Detective Sum has a list of N suspects, each carrying a certain amount of gold coins. Your task is to help Detective Sum identify the two suspects whose combined gold coins equal the value of the stolen artifact.

Input

• The first line contains two integers N and X (2 ≤ N ≤ 10^5, 1 ≤ X ≤ 10^9)
• The second line contains N integers A1, A2, ..., AN (1 ≤ Ai ≤ 10^9), where Ai is the number of gold coins the i-th suspect is carrying.

Output

Output two different integers - the indices of the two suspects (1-indexed) whose gold coins sum up to X. If there are multiple solutions, output any one of them. It is guaranteed that there is at least one solution.

Example

Input: 4 9 2 7 11 15

Output: 1 2

Explanation: Suspects 1 and 2 are carrying 2 and 7 gold coins respectively, which sum up to 9, the value of the stolen artifact.