Number of palindromic strings
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  Difficulty: Medium   Marks: 4

Derek is forming palindromic strings of length lesser than or equal to N, with first K characters of lowercase English language, such that each character in a string doesn’t appear more than twice.

Help Derek in finding out the total number of such strings formed.

 

Input:

The first line of input contains a single integer T denoting the number of test cases. Then T test cases follow. Each test case consists of two integers N and K as described in the problem statement.
 

Output:

For each test case, print in a new line, the number of such strings formed. As the results can be very large, print your answer modulo 10^9+7.

 

Constraints:

1 <= T <= 100

1 <= K <= 26

1 <= N <= 52

2*K >= N

 

Example:

Input:

2

3 2

4 3

Output:

6

18

Explanation:

For the 1st sample test case:

The possible strings are: “a”, “b”, “aa”, “bb”, “aba”, “bab”. Hence, the answer is 6.

For the 2nd sample test case:

The possible strings are: "a", "b", "c", "aa", "bb", "cc", "aba", "aca", "bab", "bcb", "cac", "cbc", "abba", "acca", "baab", "bccb", "caac", "cbbc". Hence, the answer is 18.

** For More Input/Output Examples Use 'Expected Output' option **

Contributor: Sajal Agrawal
Author: sajalagrawal


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