Description

Pascal's triangle is a triangular array of the binomial coefficients. You need to print the element k on row of Pascal's triangle, which can be calculated by the following :
C(n, 0) = 1, for n = 1, 2, …
C(n, n) = 1, for n = 1, 2, …
C(n, k) = C(n-1, k-1) + C(n-1, k),  for k = 2, 3, … and for n = 2, 3, …
 

Therefore, the first 6 rows would be

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1
 

And for example:

If n_row=3 and k_element=4, you should print 1, because the row 3 of Pascal triangle is "1 3 3 1", and 4^th number is 1.

And if n_row=6 and k_element=3, you should print 15, because the row 6 of Pascal triangle is "1 6 15 20 15 6 1", and 3^rd number is 15.
 

Note: The input n_row range is 1~25, input k_element range is 1~26.

 

Note that

1.      This problem involves three files.

• function.h: Function definition of pascalNthNum.
• function.cpp: Function describe of pascalNthNum.
• main.cpp: A driver program to test your implementation.

You will be provided with main.cpp and function.h, and asked to implement function.cpp.

2.     For OJ submission:

       Step 1. Submit only your function.cpp into the submission block. (Please choose c++ compiler) 

       Step 2. Check the results and debug your program if necessary.

function.h

void pascalNthNum(int n_row, int k_element);

main.cpp

#include <stdio.h>
#include "function.h"

int main()
{
    int row = 0;
    int kth = 0;
   
    while(scanf("%d", &row) && row != 0){
        scanf("%d", &kth);
        pascalNthNum(row, kth);
    }

    return 0;
}

Input

There are two positive integers Row (1<=Row<=25) and kth element(1 <= kth <= (Row+1)) in each line, if input Row is 0 then stop the program.

Output

Print the the kth element in the nth row.
And there is a ‘\n’ at the end of each line except input Row is 0.

Sample Input  Download

Sample Output  Download

Partial Judge Code

10829.cpp

Partial Judge Header

10829.h

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