There is a right triangle with legs of length a and b. Your task is to determine whether it is possible to locate the triangle on the plane in such a way that none of its sides is parallel to the coordinate axes. All the vertices must have integer coordinates. If there exists such a location, you have to output the appropriate coordinates of vertices.

Input

The first line contains two integers a, b (1 ≤ a, b ≤ 1000), separated by a single space.

Output

In the first line print either "YES" or "NO" (without the quotes) depending on whether the required location exists. If it does, print in the next three lines three pairs of integers — the coordinates of the triangle vertices, one pair per line. The coordinates must be integers, not exceeding 109 in their absolute value.

Examples

Input

1 1


Output

NO


Input

5 5


Output

YES
2 1
5 5
-2 4


Input

5 10


Output

YES
-10 4
-2 -2
1 2
#include <bits/stdc++.h>
using namespace std;
long long int power(long long int x, long long int y, long long int p) {
  long long int res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long int gcd(long long int a, long long int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long int lcm(long long int a, long long int b) {
  return a * b / gcd(a, b);
}
long long int max(long long int a, long long int b) {
  if (a > b) return a;
  return b;
}
long long int min(long long int a, long long int b) {
  if (a < b) return a;
  return b;
}
long long int bins(long long int arr[], long long int l, long long int r,
                   long long int x) {
  if (r >= l) {
    long long int mid = l + (r - l) / 2;
    if (arr[mid] == x) return mid;
    if (arr[mid] > x) return bins(arr, l, mid - 1, x);
    return bins(arr, mid + 1, r, x);
  }
  return -1;
}
long long int modi(long long int a, long long int m) {
  return power(a, m - 2, m);
}
long long int modeq(long long int a, long long int m) {
  return (a % m + m) % m;
}
long long int isPowerof2(int n) { return (n && !(n & (n - 1))); }
long long int collinear(long long int x1, long long int x2, long long int x3,
                        long long int y1, long long int y2, long long int y3) {
  long long int res = x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2);
  if (res == 0) {
    return 1;
  } else {
    return 0;
  }
}
int isSubstring(string s1, string s2) {
  int M = s1.length();
  int N = s2.length();
  for (int i = 0; i <= N - M; i++) {
    int j;
    for (j = 0; j < M; j++)
      if (s2[i + j] != s1[j]) break;
    if (j == M) return i;
  }
  return -1;
}
int main() {
  long long int a, b;
  cin >> a >> b;
  vector<pair<long long int, long long int> > a1;
  vector<pair<long long int, long long int> > a2;
  for (long long int i = -(a - 1); i < a - 1; i++) {
    if ((sqrt(a * a - i * i)) == (int)sqrt(a * a - i * i)) {
      a1.push_back({i, (int)sqrt(a * a - i * i)});
    }
  }
  for (long long int i = -(b - 1); i < b - 1; i++) {
    if ((sqrt(b * b - i * i)) == (int)sqrt(b * b - i * i)) {
      a2.push_back({i, (int)sqrt(b * b - i * i)});
    }
  }
  long long int f = 0;
  long long int x1, x2, y1, y2;
  for (long long int i = 0; i < a1.size(); i++) {
    for (long long int j = 0; j < a2.size(); j++) {
      if (a1[i].first != a2[j].first && a1[i].second != a2[j].second &&
          a1[i].first != 0 && a1[i].second != 0 && a2[j].first != 0 &&
          a2[j].second != 0 &&
          a1[i].first * a2[j].first == -1 * (a1[i].second * a2[j].second)) {
        x1 = a1[i].first;
        x2 = a2[j].first;
        y1 = a1[i].second;
        y2 = a2[j].second;
        f = 1;
        break;
      }
    }
    if (f == 1) {
      break;
    }
  }
  if (f == 0) {
    cout << "NO";
  }
  if (f == 1) {
    cout << "YES"
         << "\n";
    cout << 0 << " " << 0 << "\n";
    cout << x1 << " " << y1 << "\n";
    cout << x2 << " " << y2 << "\n";
  }
}
