Consider this sequence {1, 2, 3, ..., N}, as a initial sequence of first N natural numbers. You can rearrange this sequence in many ways. There will be N! different arrangements. You have to calculate the number of arrangement of first N natural numbers, where in first M (M ≤ N) positions, exactly K (K ≤ M) numbers are in its initial position. Example: For, N = 5, M = 3, K = 2 You should count this arrangement {1, 4, 3, 2, 5}, here in first 3 positions 1 is in 1-st position and 3 in 3-rd position. So exactly 2 of its first 3 are in there initial position. But you should not count this {1, 2, 3, 4, 5}. Input The first line of input is an integer T (T ≤ 1000) that indicates the number of test cases. Next T line contains 3 integers each, N (1 ≤ N ≤ 1000), M, and K. Output For each case, output the case number, followed by the answer modulo 1000000007. Look at the sample for clarification. Sample Input 1 532 Sample Output Case 1: 12