Little Bob comes to you for candies as you are his favorite coder! He wants X candies. You have N bags and the i^th bag contains A[i] candies.

You can give him a set of one or more bags such that the sum of candies in those bags is EXACTLY equal to X. Bob wants to find smallest such set of bags. If there are multiple smallest such sets than Bob wants the lexicographically smallest set of such bags.

See the sample test cases for more clarity.

Input:
The first line contains two space-separated integers N and X.
The second line contains N integers, the number of candies in each bag.

Output:
Print the indices of the bags that you give to Bob. If it is not possible to form such a set, print -1.

Constraints:
1 ≤ N ≤ 20
1 ≤ X ≤ 10⁶
1 ≤ A[i] ≤ 10⁶