Consider a money system consisting of n coins. Each coin has a positive integer value. Your task is to produce a sum of money x using the available coins in such a way that the number of coins is minimal.

For example, if the coins are \{1,5,7\} and the desired sum is 11, an optimal solution is 5+5+1 which requires 3 coins.

Input

The first input line has two integers n and x: the number of coins and the desired sum of money.

The second line has n distinct integers c_1,c_2,\dots,c_n: the value of each coin.

Output

Print one integer: the minimum number of coins. If it is not possible to produce the desired sum, print -1.

Constraints

• 1 \le n \le 100
• 1 \le x \le 10^6
• 1 \le c_i \le 10^6

Example

Input:

3 11
1 5 7

Output:

3