Luogu1641 SCOI2010生成字符串（组合数学）

　　NOI2018冒泡排序的一个子问题。

#include<iostream> 
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
#define ll long long
#define P 20100403
#define N 2000010
char getc(){char c=getchar();while ((c<'A'||c>'Z')&&(c<'a'||c>'z')&&(c<'0'||c>'9')) c=getchar();return c;}
int gcd(int n,int m){return m==0?n:gcd(m,n%m);}
int read()
{
    int x=0,f=1;char c=getchar();
    while (c<'0'||c>'9') {if (c=='-') f=-1;c=getchar();}
    while (c>='0'&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar();
    return x*f;
}
int n,m,fac[N],inv[N];
int C(int n,int m){return 1ll*fac[n]*inv[m]%P*inv[n-m]%P;}
int main()
{
#ifndef ONLINE_JUDGE
    freopen("1641.in","r",stdin);
    freopen("1641.out","w",stdout);
    const char LL[]="%I64d
";
#else
    const char LL[]="%lld
";
#endif
    n=read(),m=read();
    fac[0]=1;for (int i=1;i<=n+m;i++) fac[i]=1ll*fac[i-1]*i%P;
    inv[0]=inv[1]=1;for (int i=2;i<=n+m;i++) inv[i]=P-1ll*(P/i)*inv[P%i]%P;
    for (int i=2;i<=n+m;i++) inv[i]=1ll*inv[i-1]*inv[i]%P;
    cout<<(C(n+m,m)-C(n+m,m-1)+P)%P;
    return 0;
}