【ZJOI2017 Round1练习】D2T2 iqtest（排列组合）

题意：

思路：

根据欧拉定理，a^(phi(n)-1)为a mod n的逆元

 var prime,cnt:array[..]of longint;
     s,ans,x,mo,k,phi,tmp:int64;
     i,m,n,j:longint;

 function mult(x,y:int64):int64;
 var tmp:int64;
 begin
  tmp:=x;
  mult:=;
  while y> do
  begin
   if y and = then mult:=mult*tmp mod mo;
   tmp:=tmp*tmp mod mo;
   y:=y>>;
  end;
 end;

 function ins(x,y:longint):longint;
 var i:longint;
 begin
  for i:= to m do
   while x mod prime[i]= do
   begin
    cnt[i]:=cnt[i]+y;
    x:=x div prime[i];
   end;
  exit(x);
 end;

 begin
  assign(input,'iqtest.in'); reset(input);
  assign(output,'iqtest.out'); rewrite(output);
  readln(n,mo);
  k:=mo; phi:=mo;
  for i:= to trunc(sqrt(mo)) do
   if k mod i= then
   begin
    inc(m); prime[m]:=i; phi:=phi div i*(i-); k:=k div i;
    while k mod i= do k:=k div i;
   end;
  if k> then begin inc(m); prime[m]:=k; phi:=phi div k*(k-); end;
  s:=;
  for i:= to n do
  begin
   tmp:=s;
   for j:= to m do tmp:=tmp*mult(prime[j],cnt[j]) mod mo;
   read(x);
   ans:=(ans+tmp*x mod mo) mod mo;
   if i<n then s:=s*ins(n-i,) mod mo*mult(ins(i,-),phi-) mod mo;
  end;
  writeln(ans);
  close(input);
  close(output);
 end.