2875: [Noi2012]随机数生成器

Description
Input

包含6个用空格分割的m,a,c,X0,n和g，其中a,c,X0是非负整数，m,n,g是正整数。

Output

输出一个数，即Xn mod g
Sample Input

11 8 7 1 5 3


Sample Output
2

快速幂+快速乘

type
    matrix=array[1..2,1..2]of int64;
var
    a,c,p,x0,n,g:int64;
    x,y:matrix;
 
function kc(x,y:int64):int64;
begin
    if y=0 then exit(0);
    kc:=kc(x,y>>1);
    kc:=(kc+kc)mod p;
    if y and 1=1 then kc:=(kc+x)mod p;
end;
 
operator *(a,b:matrix)c:matrix;
var
    i,j,k:longint;
begin
    fillchar(c,sizeof(c),0);
    for i:=1 to 2 do
        for j:=1 to 2 do
            for k:=1 to 2 do
                c[i,k]:=(c[i,k]+kc(a[i,j],b[j,k]))mod p;
end;
 
procedure main;
begin
    read(p,a,c,x0,n,g);
    x[1,1]:=1;x[2,2]:=1;
    y[1,1]:=a;y[2,1]:=c;y[2,2]:=1;
    while n>0 do
        begin
            if n and 1=1 then x:=x*y;
            y:=y*y;
            n:=n>>1;
        end;
    writeln((kc(x0,x[1,1])+x[2,1])mod p mod g);
end;
 
begin
    main;
end.