The Rascal Triangle
The Rascal Triangle definition is similar to that of the Pascal Triangle. The rows are numbered from the top starting with 0. Each row n contains n+1 numbers indexed from 0 to n. Using R(n,m) to indicte the index m item in the index n row:
R(n,m) = 0 for n < 0 OR m < 0 OR m > n
The first and last numbers in each row (which are the same in the top row) are 1:
R(n,0) = R(n,n) = 1
The interior values are determined by (UpLeftEntry*UpRightEntry+1)/UpEntry (see the parallelogram in the array below):
R(n+1, m+1) = (R(n,m) * R(n,m+1) + 1)/R(n-1,m)
Write a program which computes R(n,m) theelement of therow of the Rascal Triangle.
Input
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 is a single line of input consisting of 3 space separated decimal integers. The first integer is data set number, N. The second integer is row number n, and the third integer is the index m within the row of the entry for which you are to find R(n,m) the Rascal Triangle entry (0 ≤ m ≤ n ≤ 50000).
Output
For each data set there is onr line of output. It contains the data set number N, followed by a single space which is then followed by thr Rascal Triangle entry R(n,m) accurate to the integer value.