CSES: Minimizing Coins

 Minimizing Coins

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

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

Input

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

The second line has n$n$ distinct integers c1,c2,…,cn$c_1,c_2,\dots ,c_n$: 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$-1$.

Constraints

• 1≤n≤100$1\le n\le 100$
  
• 1≤x≤106$1\le x\le {10}^6$
  
• 1≤ci≤106$1\le c_i\le {10}^6$
  

Example

Input:
3 11
1 5 7

Output:
3