Coin Change Problem

You are given a set of coin denominations and a target amount \( m \). Your task is to find the minimum number of coins required to make the amount \( m \) using any combination of the given coins. If it is not possible to form the amount, output \( -1 \).

Use the following recurrence in your solution:

\( dp[i] = \min(dp[i], dp[i-coin] + 1) \) for all coin denominations, where \( dp[i] \) represents the minimum number of coins required for amount \( i \).

Example:

• For coins = [1, 2, 5] and m = 11, the answer is 3 because \( 11 = 5 + 5 + 1 \).
• For coins = [2, 4] and m = 3, it is not possible to form 3 and the answer is \( -1 \).

inputFormat

The first line contains an integer \( T \), the number of test cases. Each test case consists of two lines:

1. The first line contains two integers \( n \) and \( m \) where \( n \) is the number of coin types and \( m \) is the target amount.
2. The second line contains \( n \) space-separated integers representing the coin denominations.

outputFormat

For each test case, output a single line containing the minimum number of coins needed to form the amount \( m \). If it is not possible, output \( -1 \).

## sample

1
3 11
1 2 5

3

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