Let’s define another number sequence, given by the following function: f(0) = a f(1) = b f(n) = f(n−1)+f(n−2), n>1 When a = 0 and b = 1, this sequence gives the Fibonacci Sequence. Changing the values of a and b, you can get many different sequences. Given the values of a, b, you have to find the last m digits of f (n). Input The first line gives the number of test cases, which is less than 10001. Each test case consists of a single line containing the integers a b n m. The values of a and b range in [0, 100], value of n ranges in [0, 1000000000] and value of m ranges in [1, 4]. Output For each test case, print the last m digits of f(n). However, you should NOT print any leading zero. Sample Input 4 0 1 11 3 0 1 42 4 0 1 22 4 0 1 21 4 Sample Output 89 4296 7711 946