Problem p01171 (C++)

Buggy submission (status: Runtime Error):
#include <algorithm>
#include <cassert>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <fstream>
#include <functional>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>

using namespace std;

#define LOG(...) printf(__VA_ARGS__)
// #define LOG(...)
#define FOR(i, a, b) for (int i = (int)(a); i < (int)(b); ++i)
#define REP(i, n) for (int i = 0; i < (int)(n); ++i)
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define EXIST(s, e) ((s).find(e) != (s).end())
#define SORT(c) sort((c).begin(), (c).end())
#define RSORT(c) sort((c).rbegin(), (c).rend())
#define CLR(a) memset((a), 0, sizeof(a))

typedef long long ll;
typedef unsigned long long ull;
typedef vector<bool> vb;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<vb> vvb;
typedef vector<vi> vvi;
typedef vector<vll> vvll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};
bool b[1000001] = {false};
int main() {
  vector<int> prime;
  FOR(i, 2, 10001) {
    if (!b[i]) {
      for (int j = i + i; j < 1001; j += i) {
        b[j] = true;
      }
      prime.push_back(i);
    }
  }
  int n, m;
  while (cin >> n >> m, n) {
    int count = 0;
    vector<int> np;
    while (n != 1) {
      if (n % prime[count] == 0) {
        if (np.size() == 0 || prime[count] != np[np.size() - 1])
          np.push_back(prime[count]);
        n /= prime[count];
      } else {
        count++;
      }
    }
    vector<int> mp;
    count = 0;
    while (m != 1) {
      if (m % prime[count] == 0) {
        if (mp.size() == 0 || prime[count] != mp[mp.size() - 1])
          mp.push_back(prime[count]);
        m /= prime[count];
      } else {
        count++;
      }
    }
    int ansn = np[np.size() - 1];
    int ansm = mp[mp.size() - 1];
    REP(i, np.size() - 1) { ansn -= np[i]; }
    REP(i, mp.size() - 1) { ansm -= mp[i]; }
    string anss = (ansn > ansm) ? "a" : "b";
    cout << anss << endl;
  }
}

Fixed submission:
#include <algorithm>
#include <cassert>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <fstream>
#include <functional>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>

using namespace std;

#define LOG(...) printf(__VA_ARGS__)
// #define LOG(...)
#define FOR(i, a, b) for (int i = (int)(a); i < (int)(b); ++i)
#define REP(i, n) for (int i = 0; i < (int)(n); ++i)
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define EXIST(s, e) ((s).find(e) != (s).end())
#define SORT(c) sort((c).begin(), (c).end())
#define RSORT(c) sort((c).rbegin(), (c).rend())
#define CLR(a) memset((a), 0, sizeof(a))

typedef long long ll;
typedef unsigned long long ull;
typedef vector<bool> vb;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<vb> vvb;
typedef vector<vi> vvi;
typedef vector<vll> vvll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};
bool b[1000001] = {false};
int main() {
  vector<int> prime;
  FOR(i, 2, 1000001) {
    if (!b[i]) {
      for (int j = i + i; j < 1001; j += i) {
        b[j] = true;
      }
      prime.push_back(i);
    }
  }
  int n, m;
  while (cin >> n >> m, n) {
    int count = 0;
    vector<int> np;
    while (n != 1) {
      if (n % prime[count] == 0) {
        if (np.size() == 0 || prime[count] != np[np.size() - 1])
          np.push_back(prime[count]);
        n /= prime[count];
      } else {
        count++;
      }
    }
    vector<int> mp;
    count = 0;
    while (m != 1) {
      if (m % prime[count] == 0) {
        if (mp.size() == 0 || prime[count] != mp[mp.size() - 1])
          mp.push_back(prime[count]);
        m /= prime[count];
      } else {
        count++;
      }
    }
    int ansn = np[np.size() - 1];
    int ansm = mp[mp.size() - 1];
    REP(i, np.size() - 1) { ansn -= np[i]; }
    REP(i, mp.size() - 1) { ansm -= mp[i]; }
    string anss = (ansn > ansm) ? "a" : "b";
    cout << anss << endl;
  }
}