# Stick Break Codechef Solution

### We Are Discuss About CODECHEF SOLUTION

Stick Break Codechef Solution

## Problem

Chef has a stick of length L. Chef wants to break the stick into K parts such that each part has a non-zero length.

Let the lengths of the K parts be A_1, A_2, \ldots, A_K (Note that A_1 + A_2 + \ldots + A_K = L and A_i is a positive integer for all i). Chef wants to minimize the value of \displaystyle \sum_{i = 1}^{K – 1}|A_{i + 1} – A_i|. Can you help Chef? (Here |x| denotes the absolute value of x)

Under the given constraints it will always be possible to break the stick into K parts of non-zero lengths.

### Input Format

• The first line contains a single integer T — the number of test cases. Then the test cases follow.
• The first and only line of each test case contains two space-separated integers L and K — the initial length of the stick and the number of parts Chef wants to break the stick into.

### Output Format

For each test case, output the minimum value of \displaystyle \sum_{i = 1}^{K – 1}|A_{i + 1} – A_i|.

### Constraints

• 1 \leq T \leq 10^4
• 2 \le K \le L \le 10^9

### Sample 1:

Input

Output

2
4 3
2 2

1
0


### Explanation:

Test Case 1: It is optimal to break the stick of length 4 into 3 parts in the following manner: [2, 1, 1]. The value of \displaystyle \sum_{i = 1}^{K – 1}|A_{i + 1} – A_i| = |1 – 2| + |1 – 1| = 1.

Test Case 2: It is optimal to break the stick of length 2 into 2 parts in the following manner: [1, 1]. The value of \displaystyle \sum_{i = 1}^{K – 1}|A_{i + 1} – A_i| = |1 – 1| = 0.

## Stick Break Codechef Solution

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