Coin Change

You are given an integer array coins representing coins of different denominations and an integer amount representing a total amount of money.

Return the fewest number of coins that you need to make up that amount. If that amount of money cannot be made up by any combination of the coins, return -1.

You may assume that you have an infinite number of each kind of coin.

Visualizations & Examples:

Optimal Subarray & DP Transition for Example 1:

Explanation for Example 1: To make 11¢ using coins [1, 2, 5], the optimal minimum path uses two 5¢ coins and one 1¢ coin (total 3 coins). The DP array tracks the minimum coin count needed to compose every integer value up to the target amount.

Input Format:

Line 1: Two space-separated integers: N (size of coins array) and amount (target amount).
Line 2: N space-separated integers representing the coin denominations.

Output Format:

Print a single integer: the fewest number of coins needed to make the amount, or -1 if unreachable.

Constraints:

1 ≤ coins.length ≤ 12
1 ≤ coins[i] ≤ 2^31 - 1
0 ≤ amount ≤ 10^4

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