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

Example Output

3