581. Coin Change II

0

Medium

You are given an integer array coins representing coins of different denominations and an integer amount representing a total amount of money.
Print the number of combinations that make up that amount. If that amount of money cannot be made up by any combination of the coins, return 0.
You may assume that you have an infinite number of each kind of coin.
The answer is guaranteed to fit into a signed 32-bit integer.

Input Format

First Line Contains amount

Second Line contains size of array

Third line contains elements of array

Second Line contains size of array

Third line contains elements of array

Output Format

Print the amount (Integer)

Example

Input

5
3
1 2 5

Output

4

Constraints

1 <= coins.length <= 300

1 <= coins[i] <= 5000

All the values of coins are unique.

0 <= amount <= 5000

1 <= coins[i] <= 5000

All the values of coins are unique.

0 <= amount <= 5000

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