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 indicate 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)

1

1 1

1 2 1

/ \

1 3 3 1

\ /

1 4 5 4 1

Write a program which computes R(n, m) the m^th element of the n^th row of the Rascal Triangle.

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).

For each data set there is one line of output. It contains the data set number, N, followed by a single space which is then followed by the Rascal Triangle entry R(n, m) accurate to the nearest integer value.