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Count Coin Combinations

Count ways to make an amount with unlimited coins of specified denominations.

Use any number of each supplied denomination to make amount exactly. Count combinations, not orderings: two arrangements using the same counts of each coin are the same way. Denominations are distinct and positive.

Implement coin_sums(amount, coins).

Input

amount: The total amount to make.

coins: The available distinct denominations.

Output

Return the number of unordered combinations.

制約

0 ≤ amount ≤ 200. There are 0 through 10 distinct denominations, each from 1 through 200. All counts fit signed 64-bit. Amount 0 has one way: choose no coins.

例

例 1
入力:
coins = [1, 2]
amount = 4

期待される出力:
expected = 3
入力:
std::vector<long long> coins = {1, 2};
long long amount = 4;

期待される出力:
long long expected = 3;
入力:
long[] coins = new long[] {1, 2};
long amount = 4;

期待される出力:
long expected = 3;

解説

The combinations are four 1s, two 1s with one 2, and two 2s.

例 2
入力:
coins = [2]
amount = 3

期待される出力:
expected = 0
入力:
std::vector<long long> coins = {2};
long long amount = 3;

期待される出力:
long long expected = 0;
入力:
long[] coins = new long[] {2};
long amount = 3;

期待される出力:
long expected = 0;

解説

Any sum of 2-valued coins is even, so 3 is impossible.

参考資料

この課題はCodeUtility用に調整されています。上記の説明と制約に従ってください。

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