Codevs 1137 Calculation Factor 2011 NOIP National League Improvement Group

1137 Calculation factor 2011 NOIP National League Increase group
time limit: 1 s
Space limit: 128000 KB
Title level: Gold Gold
Title Description Descripti On
Given a polynomial (ax + by) ^k, the coefficients of x^n y^m items are requested after the expansion of the polynomial. The
Input description input Description
contains a total of 5 integers, each of which is a,b,k,n,m, separated by a space between each of the two integers. The
Output description output Description
Outputs a total of 1 rows, containing an integer representing the coefficients to be obtained, which may be large, and the output will result in 10007 modulo.
Sample Input Sample inputs
1 1 3 1 2
Sample outputs sample output
3
data range and hints Data Size & Hint
Data range
for 3 0% of the data, there are 0≤k≤10;
for 50% of the data, there is a = 1,b = 1;
for 100% of the data, there is 0≤k≤1,000,0≤n, m≤k, and n + M = k,0≤a,b≤1,000,000.
Category Tags Tags
continental Noip National League increase 2011

/* Yang Hui triangle + fast power. In fact, you can push it yourself. And then what bothers me is that the problem can be directly with a and b when the initial factor runs the Yang Hui Triangle. Oh, ah, the brain is low. */#include <iostream> #include <cstdio> #define MAXN 1010 #define MOD 10007 #define LL long Long using NAMESPAC
e std;
int F[MAXN][MAXN];
int a1,b1,k,m,n;
int ans;
    ll mi (ll A,ll b) {ll tot=1;
        while (b) {if (b&1) tot= (tot*a)%mod;
        A= (a*a)%mod;
    b>>=1;
} return tot;
    } void Slove () {for (int i=1;i<=k;i++) f[i][1]=f[i][i+1]=1;
        for (int i=2;i<=k;i++) for (int j=2;j<=i;j++) {f[i][j]= (f[i-1][j]+f[i-1][j-1])%mod;
    } Ans=f[k][k-n+1]%mod;
    if (n) ans= (Ans*mi (a1%mod,n))%mod;
    if (m) ans= (Ans*mi (b1%mod,m))%mod;
printf ("%d", ans%mod);
    } int main () {scanf ("%d", &A1);cin>>b1>>k>>n>>m;
    Slove ();
return 0; }