7541: [CSES Problem Set] Coin Combinations I
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Description
Consider a money system consisting of $n$ coins. Each coin has a positive integer value. Your task is to calculate the number of distinct ways you can produce a money sum $x$ using the available coins.
For example, if the coins are $\{2,3,5\}$ and the desired sum is $9$, there are $8$ ways:
For example, if the coins are $\{2,3,5\}$ and the desired sum is $9$, there are $8$ ways:
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2+2+5
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2+5+2
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5+2+2
-
3+3+3
-
2+2+2+3
-
2+2+3+2
-
2+3+2+2
- 3+2+2+2
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.
The second line has $n$ distinct integers $c_1,c_2,\dots,c_n$: the value of each coin.
Output
Print one integer: the number of ways modulo $10^9+7$.
Constraints
$1≤n≤100$
$1 \le x \le 10^6$
$1 \le c_i \le 10^6$
$1 \le x \le 10^6$
$1 \le c_i \le 10^6$
Sample 1 Input
3 9
2 3 5
Sample 1 Output
8