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Minimum cost to fill given weight in a bag
     

You are given a bag of size W kg and you are provided costs of packets different weights of oranges in array cost[] where cost[i] is basically cost of ‘i’ kg packet of oranges. Where cost[i] = -1 means that ‘i’ kg packet of orange is unavailable

Find the minimum total cost to buy exactly W kg oranges and if it is not possible to buy exactly W kg oranges then print -1. It may be assumed that there is infinite supply of all available packet types.

Note : array starts from index 1.

Input:
The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. The first line of each test case contains integers N and W where N denotes the size of array cost[ ] and W is the size of the bag.

The second line of each test case contains N space separated integers denoting elements of the array cost[ ].


Output:

Print the minimum cost to buy exactly W kg oranges. If no such answer exists print "-1".


Constraints:

1<= T <=100

1<= N, W <=1000

1<= cost[ ] <=1000 


Example:

Input:

2

5 5

20 10 4 50 100

5 5

-1 -1 4 5 -1

Output:

14

-1

 

** For More Input/Output Examples Use 'Expected Output' option **

Contributor: Sujnesh Mishra

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