【BZOJ2982】combination（Lucas定理）

题意：求C(n,m)

n,m<=200000000

思路：c(n,m)=c(n mod mo,m mod mo)*c(n div mo,m div mo) mod mo (n>=mo或m>=mo)

c(x,y)=0 (x<y)

c(n,m)=fac[n]*exf[m]*exf[n-m] (n,m<mo)

const mo=10007;
var exf,fac:array[0..1000000]of longint;
    n,i,x,y:longint;

function c(n,m:longint):longint;
begin
 if n<m then exit(0);
 if (n<mo)and(m<mo) then exit(fac[n]*exf[m] mod mo*exf[n-m] mod mo);
 exit(c(n mod mo,m mod mo)*c(n div mo,m div mo) mod mo);
end;

begin
 assign(input,'bzoj2982.in'); reset(input);
 assign(output,'bzoj2982.out'); rewrite(output);
 readln(n);
 exf[0]:=1; exf[1]:=1; fac[0]:=1; fac[1]:=1;
 for i:=2 to 1000000 do
 begin
  exf[i]:=exf[mo mod i]*(mo-mo div i) mod mo;
  fac[i]:=fac[i-1]*i mod mo;
 end;
 for i:=1 to 1000000 do exf[i]:=exf[i-1]*exf[i] mod mo;

 for i:=1 to n do
 begin
  readln(x,y);
  writeln(c(x,y));
 end;
 close(input);
 close(output);
end.