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 Specification

• 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 Specification

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

Constrains

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

Sample Cases

Input #1:

3 11
1 5 7

Output #1:

3