시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 512 MB 2 1 1 50.000%

문제

Given a positive integer, N, a permutation of order N is a one-to-one (and thus onto) function from the set of integers from 1 to N to itself. If p is such a function, we represent the function by a list of its values:

[ p(1) p(2) … p(N) ]

For example,

[5 6 2 4 7 1 3] represents the function from { 1 … 7 } to itself which takes 1 to 5, 2 to 6, … , 7 to 3.

For any permutation p, a descent of p is an integer k for which p(k) > p(k+1). For example, the permutation [5 6 2 4 7 1 3] has a descent at 2 (6 > 2) and 5 (7 > 1).

For permutation p, des(p) is the number of descents in p. For example, des([5 6 2 4 7 1 3]) = 2. The identity permutation is the only permutation with des(p) = 0. The reversing permutation with p(k) = N+1-k is the only permutation with des(p) = N-1.

The permutation descent count (PDC) for given order N and value v is the number of permutations p of order N with des(p) = v. For example:

  • PDC(3, 0) = 1 { [ 1 2 3 ] }
  • PDC(3, 1) = 4 { [ 1 3 2 ], [ 2 1 3 ], [ 2 3 1 ], 3 1 2 ] }
  • PDC(3, 2) = 1 { [ 3 2 1 ] }

Write a program to compute the PDC for inputs N and v. To avoid having to deal with very large numbers, your answer (and your intermediate calculations) will be computed modulo 1001113.

입력

The first line of input contains a single integer P, (1 ≤ P ≤ 1000), which is the number of data sets that follow. Each data set should be processed identically and independently.

Each data set consists of a single line of input. It contains the data set number, K, followed by the integer order, N (2 ≤ N ≤ 100), followed by an integer value, v (0 ≤ v ≤ N-1).

출력

For each data set there is a single line of output. The single output line consists of the data set number, K, followed by a single space followed by the PDC of N and v modulo 1001113 as a decimal integer.

예제 입력 1

4
1 3 1
2 5 2
3 8 3
4 99 50

예제 출력 1

1 4
2 66
3 15619
4 325091