Coin Combinations I CSES dynamic programming problem set solution

 Coin Combinations I CSES dynamic programming problem set solution -

Problem statement-

Consider a money system consisting of n$n$ coins. Each coin has a positive integer value. Your task is to calculate the number of distinct ways you can produce a money sum x$x$ using the available coins.

For example, if the coins are {2,3,5}$\{2,3,5\}$ and the desired sum is 9$9$, there are 8$8$ ways:

• 2+2+5$2+2+5$
  
• 2+5+2$2+5+2$
  
• 5+2+2$5+2+2$
  
• 3+3+3$3+3+3$
  
• 2+2+2+3$2+2+2+3$
  
• 2+2+3+2$2+2+3+2$
  
• 2+3+2+2$2+3+2+2$
  
• 3+2+2+2$3+2+2+2$
  

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 number of ways modulo 109+7${10}^9+7$.

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 9
2 3 5

Output:
8




Code Solution -