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