Data type for ....JUST ADD IT

[iit2011101]

problem: spoj.pl/problems/ZSUM/
help is required related to wat datatype to be use??
i used unsigned long long int in this code .. its wrking for sum given inputs but not for alll..

#include <stdio.h>
#include <math.h>
#include <stdlib.h>
long long int mod ( long long int z ) 
{
    z  = z%10000007;
if ( z < 10000007 ) {
	return z;
}
else {
	z = mod(z);
}
}
unsigned long long int s( long int n, long int k )
{
	unsigned long long int sum = 0;
	long int i;
	for (  i  = 1; i <= n; i++ ) {
		sum = sum + pow(i,k);
	}
	return sum;
}
unsigned long long int p( long  int n ) 
{
	unsigned long long int sum = 0;
	 long int i;
	for (  i = 1; i <= n; i++ ) {
		sum = sum + pow(i,i);
	}
	return sum;
}
int main()
{
	long int n;
	long int k;
	long int z;
	int c;
	int count;
	unsigned long long int sum;
    scanf("%lld",&n);
scanf("%lld",&k);

while ( n != 0 && k != 0 ) {


c = 1;
sum  = 0;
z = s(n,k) + p(n);
n = n-1;
sum = sum + z ;
count = 1;
while ( n > 1 && count < 3 ) {
	z = s(n,k) + p(n);
	if ( c % 2 != 0 ) {
		sum = sum + c*z ;
	}
	else {
		sum = sum + (-c)*z ;
	}
	c++;
	n--;
	count++;
}
if ( sum < 100000007){
	
	printf("%lld\n",sum);
}
else {
	printf("%lld\n", mod(sum));
}
scanf("%lld",&n);
scanf("%lld",&k);
}
return 0;
}