Program to find factorials for given test cases

Question

Input
An integer t, 1<=t<=100, denoting the number of test cases, followed by t lines, each containing a single integer n, 1<=n<=100.

Output
For each integer n given at input, display a line with the value of n!

I have typed the code below and it doesn't get accepted on codechef.
I don't know why.

#include<stdio.h>
double fact(int n);
void disp(double t);

int main() {
  int a, i, c[100];
  scanf("%d", &a);
  for (i = 0; i < a; i++) {
    scanf("%d", &c[i]);
  }
  for (i = 0; i < a; i++) {
    disp(fact(c[i]));
  }
  return 0;
}

double fact(int n) {
  double f;
  if (n == 1 || n == 0)
    f = (double) 1;
  else
    f = (double) n * fact(n - 1);
  return f;
}

void disp(double t) {
  printf("%f\n", t);
}

Answer 1

I have typed the code below and it doesn't get accepted on codechef.
I don't know why.

OP's code fails as double lacks precision for this task. Given "containing a single integer n, 1<=n<=100." and fact(100), the printed result needs far more precision than afforded by double.

---

100! is exactly

93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

double (precision) and uint64_t (range) are both insufficient for this task. Need new approach. Something that extends exact integer multiplication.

Perhaps create a function that multiplies a string? mult_str(char *s, int n)? "1" * 2 --> "2".

Do-able in about 30 lines of C code without special libraries.