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#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <stdint.h>
#define C 9901
uint64_t sumdiv(uint64_t n);
uint64_t binexp(uint64_t a, uint64_t b);
int egcd(int a, int b, int *x, int *y);
uint64_t invers_mod(uint64_t x, uint64_t m);
int main(void)
{
FILE *in = fopen("sumdiv.in", "r");
FILE *out = fopen("sumdiv.out", "w");
if(in != NULL && out != NULL)
{
uint64_t a, b;
fscanf(in, "%llu%*c%llu%*c", &a, &b);
fprintf(out, "%llu\n", sumdiv(binexp(a, b)));
fclose(in);
fclose(out);
}
else
{
printf("file error\n");
}
return 0;
}
uint64_t invers_mod(uint64_t x, uint64_t m)
{
int s, f;
int d = egcd(x, m, &s, &f);
if(d == 1)
{
return (s % m + m) % m;
}
else
{
printf("No invers moduloar\n\n");
}
}
int egcd(int a, int b, int *x, int *y)
{
if(a == 0)
{
*x = 0;
*y = 1;
return b;
}
else
{
int x1, y1;
int d = egcd(b % a, a, &x1, &y1);
*x = y1 - (b / a) * x1;
*y = x1;
return d;
}
}
uint64_t binexp(uint64_t x, uint64_t n)
{
if(n == 1)
{
return x % C;
}
uint64_t res = 1;
while(n > 0)
{
if(n % 2 != 0)
{
res = ((res % C) * (x % C)) % C;
}
x = ((x % C) * (x % C)) % C;
n /= 2;
}
return res;
}
uint64_t sumdiv(uint64_t n)
{
uint64_t res = 1, d = 2;
while(n > 1)
{
uint64_t p = 0;
while(n % d == 0)
{
p++;
n /= d;
}
if(p)
{
// printf("q: %llu %llu\n", d, p);
// uint64_t iv = invers_mod(d - 1, C);
// uint64_t r = (((binexp(d, p) - 1) % C) * (iv % C)) % C;
// res = ((res % C) * (r % C)) % C;
uint64_t s = 1;
uint64_t j = 1;
for(; j <= p; j++)
{
s = ((s % C) + (binexp(d, j) % C)) % C;
}
res = ((res % C) * (s % C)) % C;
}
d++;
if(n > 1 && d * d > n)
{
d = n;
}
}
return res;
}