Digit Count

Medium

LOJ-1122

Given a set of digits S, and an integer n, you have to find how many n-digit integers are there, which contain digits that belong to S and the difference between any two adjacent digits is not more than two.

Input

Input starts with an integer T (≤ 300), denoting the number of test cases.

Each case contains two integers, m (1 ≤ m < 10) and n (1 ≤ n ≤ 10). The next line will contain m integers (from 1 to 9) separated by spaces. These integers form the set S as described above. These integers will be distinct and given in ascending order.

Output

For each case, print the case number and the number of valid n-digit integers in a single line.

Sample

Sample Input	Sample Output
Click to copy 3 3 2 1 3 6 3 2 1 2 3 3 3 1 4 6	Click to copy Case 1: 5 Case 2: 9 Case 3: 9

Notes

For the first case the valid integers are

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#include <bits/stdc++.h>
using namespace std;
​
// Reads two integers and prints their sum
void basicIO() {
    int a, b;
    cin >> a >> b;
    cout << a + b << endl;
}
​
int main() {
    // basicIO();
    // Your cpp code here
    return 0;
}
​

Input

Output

Sample

Notes

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