# UVA 10943How Do you add? (Simple combination)

Source: Internet
Author: User
problem a:how Do you add?Larry is very bad at Math-he usually uses a calculator, which worked well throughout college. Unforunately, he is now struck in a deserted and his good buddy Ryan after a snowboarding accident. They ' re now trying to spend some time figuring out some good problems, and Ryan would eat Larry if he cannot answer, so he Fate is up to you!

It's a very simple problem-given a number N, what many ways can K numbers less than n add up to n?

For example, for N = 2 and K = +, there is ways:
0+20
1+19
2+18
3+17
4+16
5+15
...
18+2
19+1
20+0

InputEach line would contain a pair of numbers N and K. N and K would both be a integer from 1 to inclusive. The input would terminate on 2 0 ' s. OutputSince Larry is only interested in the last few digits of the answer, for each pair of numbers N and K, print a single Number mod 1,000,000 on a.

Sample Input
```2
2
0 0
```
Sample Output
`21`
`Test instructions: give you n and K, so that you can find the number of K and N of the species (0); Obviously the plate method, the n is considered as N 1, because it can be 0, so also add K 0, that is 1 1 1 1 ... 0 0 0 0, then a total of n+k-1 empty, insert K-1 board, so the final result`
`Code:`
```#include <iostream>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <vector>
#include <stdlib.h>
#include <string>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <set>
# Define INF 0x3f3f3f3f
#define EPS 1e-5
#define MAX (a) > (b)? ( A):(B)
#define MIN (a) (a) < (b)? ( A):(B)
#define N
#define MOD 1000000
using namespace std;
int c[n+1][n+1];
void init ()
{
int i,j;
C[0][0]=1;
for (i=1;i<=n;i++)
{
c[i][0]=1;
for (j=1;j<n;j++)
{
c[i][j]= (c[i-1][j]%mod+c[i-1][j-1]%mod)%mod;
}
c[i][n]=1;
}
}
int main ()
{
int n,k,ans,i;
Init ();
while (~SCANF ("%d%d", &n,&k) && (n| | k)
{
printf ("%d\n", C[n+k-1][k-1]);
}
return 0;
}```

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