#include<iostream>#include<cstdio>#include<algorithm>#include<cstring>#include<map>#include<cmath>#include<string>#include<vector>using namespace std;const int M = 300;int t,a,b;char* toString(int x){ char *res = new char[M]; memset(res,0,M); int i = 0; while(x) { res[i++] = x % 10 + '0'; x /= 10; } return res;}char* multi(char* a, char* b){ char *res = new char[M]; memset(res,0,M); int lena = strlen(a), lenb = strlen(b); for (int i = 0;i<lena; i++) { int last = 0; for (int j = 0; j<lenb; j++) { res[i + j] += (a[i] - '0') * (b[j] - '0') + last; last = res[i + j] / 10; res[i + j] %= 10; } for (int j = lenb + i;last;j++) { res[j] += last; last = res[j] / 10; res[j] %= 10; } } int lenres = M - 1; for (int i = M - 1;i>=0;i--) res[i] += '0'; while(res[--lenres] == '0') res[lenres] = 0; return res;}char* pow(char* a, int b){ char* res = toString(1), *tmp; while(b) { if (b & 1) { tmp = multi(res, a); delete res; res = tmp; } tmp = multi(a,a); delete a; a = tmp; b >>= 1; } delete a; return res;}char* add(char* a, char* b){ if (strlen(a) < strlen(b)) { swap(a,b); } int lena = strlen(a), lenb = strlen(b); char* res = new char[M]; memset(res,0,M); int last = 0; for (int i = 0;i<lenb;i++) { res[i] = a[i] + b[i] + last -'0' -'0'; last = res[i] / 10; res[i] %= 10; } for (int i = lenb; i < lena;i++) { res[i] = a[i] + last - '0'; last = res[i] / 10; res[i] %= 10; } if (last) res[lena] = last + '0'; int lenres = M - 1; for (int i = M - 1;i>=0;i--) res[i] += '0'; while(res[--lenres] == '0') res[lenres] = 0; return res;}int main(){ while(scanf("%d%d%d",&t,&a,&b)==3) { printf("(%d^%d-1)/(%d^%d-1) ",t,a,t,b); if (t==1 || a%b || (long long)(log10(t+0.)*(a-b))+1>=100LL) { puts("is not an integer with less than 100 digits."); } else { if(a == b) { puts("1"); continue; } int tmp = a / b; char *in,*m,*more = pow(toString(t), b); in = toString(0); m = toString(1); for (int i = 0;i < tmp; i++) { char* tmp = add(in,m); delete in; in = tmp; tmp = multi(m, more); delete m; m = tmp; } for (int i = strlen(in) - 1;i>=0;i--) { putchar(in[i]); } puts(""); delete in; delete m; delete more; } } return 0;}
