USACO 1.4 Arithmetic Progression

Brutal force, pretty ugly code. Need optimize.

#include <iostream>
#include <fstream>
#include <iterator>
#include <vector>
#include <string>
#include <cctype>
#include <algorithm>

using namespace std;

int main() {
  ifstream fin("ariprog.in");
  ofstream fout("ariprog.out");
  int const SIZE = 250;
  int N, M;
  fin >> N >> M;

  vector<bool> set(SIZE * SIZE * 2 + 1, false);
  for (int i = 0; i <= M; ++i) {
    for (int j = 0; j <= M; ++j) {
      set[i * i + j * j] = true;
    }
  }

  vector<pair<int, int>> result;
  auto limit = M * M * 2;
  for (int i = 0; i < limit; ++i) {
    bool found = true;
    for (int j = 1; j < limit - i; ++j) {
      if (j * (N - 1) + i > limit) {
        found = false;
        break;
      }

      for (int k = N - 1; k >= 0; --k) {
        auto val = i + k * j;

        if (val > limit) {
          found = false;
          break;
        }

        if (!set[val]) {
          found = false;
          break;
        } else {
          found = true;
        }
      }
      if (found) {
        result.emplace_back(std::make_pair(i, j));
      }
    }
  }

  sort(result.begin(), result.end(), [] (const pair<int, int> &lhs,
                                         const pair<int, int> &rhs) {
    return lhs.second != rhs.second ? lhs.second < rhs.second : lhs.first < rhs.first;
  });

  for (auto item : result) {
    fout << item.first << " " << item.second << std::endl;
  }

  if (!result.size())
    fout << "NONE" << endl;

  return 0;
}