Description

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  OR m  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 mth element of the nth row 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 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.

Sample

Input

5
1 4 0
2 4 2
3 45678 12345
4 12345 9876
5 34567 11398

Output

1 1
2 5
3 411495886
4 24383845
5 264080263