You are given an integer array coins representing coins of different denominations and an integer k.
You have an infinite number of coins of each denomination. However, you are not allowed to combine coins of different denominations.
\n\nReturn the kth smallest amount that can be made using these coins.
\n
Example 1:
\n\nInput: coins = [3,6,9], k = 3
\n\nOutput: 9
\n\nExplanation: The given coins can make the following amounts:
\nCoin 3 produces multiples of 3: 3, 6, 9, 12, 15, etc.
\nCoin 6 produces multiples of 6: 6, 12, 18, 24, etc.
\nCoin 9 produces multiples of 9: 9, 18, 27, 36, etc.
\nAll of the coins combined produce: 3, 6, 9, 12, 15, etc.
Example 2:
\n\nInput: coins = [5,2], k = 7
\n\nOutput: 12
\n\nExplanation: The given coins can make the following amounts:
\nCoin 5 produces multiples of 5: 5, 10, 15, 20, etc.
\nCoin 2 produces multiples of 2: 2, 4, 6, 8, 10, 12, etc.
\nAll of the coins combined produce: 2, 4, 5, 6, 8, 10, 12, 14, 15, etc.
\n
Constraints:
\n\n1 <= coins.length <= 151 <= coins[i] <= 251 <= k <= 2 * 109coins contains pairwise distinct integers.给你一个整数数组 coins 表示不同面额的硬币，另给你一个整数 k 。
你有无限量的每种面额的硬币。但是，你 不能 组合使用不同面额的硬币。
\n\n返回使用这些硬币能制造的 第 kth 小 金额。
\n\n
示例 1：
\n\n输入： coins = [3,6,9], k = 3
\n\n输出： 9
\n\n解释：给定的硬币可以制造以下金额：
\n3元硬币产生3的倍数：3, 6, 9, 12, 15等。
\n6元硬币产生6的倍数：6, 12, 18, 24等。
\n9元硬币产生9的倍数：9, 18, 27, 36等。
\n所有硬币合起来可以产生：3, 6, 9, 12, 15等。
示例 2：
\n\n输入：coins = [5,2], k = 7
\n\n输出：12
\n\n解释：给定的硬币可以制造以下金额：
\n5元硬币产生5的倍数：5, 10, 15, 20等。
\n2元硬币产生2的倍数：2, 4, 6, 8, 10, 12等。
\n所有硬币合起来可以产生：2, 4, 5, 6, 8, 10, 12, 14, 15等。
\n\n
提示：
\n\n1 <= coins.length <= 151 <= coins[i] <= 251 <= k <= 2 * 109coins 包含两两不同的整数。x.",
"Use the inclusion-exclusion principle to count the number of distinct amounts that can be made up to x."
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