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.x.",
"Use the inclusion-exclusion principle to count the number of distinct amounts that can be made up to x."
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