Coin Change II

You are given coins of different denominations and a total amount of money amount. Write a function to compute 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.

Input

  • coins: A list of the coins and their denominations.
  • amount: The target amount

Output

The number of combinations that make up that amount.

Examples

Example 1:

Input:

1coins = [1, 2, 5]
2amount = 5

Output: 4

Explanation:

There are four ways to make up the amount:

  • 5 = 5
  • 5 = 2 + 2 + 1
  • 5 = 2 + 1 + 1 + 1
  • 5 = 1 + 1 + 1 + 1 + 1

Example 2:

Input:

1coins = [2]
2amount = 3

Output: 0

Explanation:

The amount of 3 cannot be made up with just coins of 2.

Constraints

  • 1 <= len(coins) <= 300
  • 1 <= amount <= 5000
  • 1 <= coins[i] <= 5000

Try it yourself

Solution