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;
struct debugger {
  template <typename T>
  debugger &operator,(const T &v) {
    cerr << v << " ";
    return *this;
  }
} dbg;
inline long long gcd(long long a, long long b) {
  a = ((a) < 0 ? -(a) : (a));
  b = ((b) < 0 ? -(b) : (b));
  while (b) {
    a = a % b;
    swap(a, b);
  }
  return a;
}
long long ext_gcd(long long A, long long B, long long *X, long long *Y) {
  long long x2, y2, x1, y1, x, y, r2, r1, q, r;
  x2 = 1;
  y2 = 0;
  x1 = 0;
  y1 = 1;
  for (r2 = A, r1 = B; r1 != 0;
       r2 = r1, r1 = r, x2 = x1, y2 = y1, x1 = x, y1 = y) {
    q = r2 / r1;
    r = r2 % r1;
    x = x2 - (q * x1);
    y = y2 - (q * y1);
  }
  *X = x2;
  *Y = y2;
  return r2;
}
inline long long modInv(long long a, long long m) {
  long long x, y;
  ext_gcd(a, m, &x, &y);
  x %= m;
  if (x < 0) x += m;
  return x;
}
inline long long power(long long a, long long p) {
  long long res = 1, x = a;
  while (p) {
    if (p & 1) res = (res * x);
    x = (x * x);
    p >>= 1;
  }
  return res;
}
inline long long bigmod(long long a, long long p, long long m) {
  long long res = 1 % m, x = a % m;
  while (p) {
    if (p & 1) res = (res * x) % m;
    x = (x * x) % m;
    p >>= 1;
  }
  return res;
}
inline int STRLEN(char *s) {
  int p = 0;
  while (s[p]) p++;
  return p;
}
const long long inf = 2147383647;
const long long mod = 1000000007;
const double pi = 2 * acos(0.0);
const double eps = 1e-9;
const int Size = 205;
long long a, b;
long long xx1, xx2, yy1, yy2, xx3 = 0, yy3 = 0;
;
bool ok() {
  if (((xx1 - xx3) * (xx1 - xx3)) + ((yy1 - yy3) * (yy1 - yy3)) +
          ((xx2 - xx3) * (xx2 - xx3)) + ((yy2 - yy3) * (yy2 - yy3)) ==
      ((xx1 - xx2) * (xx1 - xx2)) + ((yy1 - yy2) * (yy1 - yy2)))
    return true;
  return false;
}
long long getSqrt(long long val) {
  long long sqr = sqrt(val);
  if (((sqr) * (sqr)) == val) {
    return sqr;
  } else if (((sqr + 1) * (sqr + 1)) == val) {
    return sqr + 1;
  } else if (((sqr + 2) * (sqr + 2)) == val) {
    return sqr + 2;
  } else {
    return -1;
  }
}
bool solve2(long long a, long long b) {
  xx2 = -max(a, b);
  for (int c = 0; c <= 3 * max(a, b); c++, xx2++) {
    if (xx2 == xx1 || xx2 == xx3) continue;
    long long rem = b * b - xx2 * xx2;
    if (rem < 0) continue;
    yy2 = getSqrt(rem);
    if (yy2 == -1) continue;
    if (yy2 == yy1 || yy2 == yy3) continue;
    if (ok() == true) {
      return true;
    }
  }
  return false;
}
bool solve(long long a, long long b) {
  xx1 = -max(a, b);
  for (int c = 0; c <= 2 * max(a, b); c++, xx1++) {
    if (xx1 == xx3) continue;
    long long rem = a * a - xx1 * xx1;
    if (rem < 0) continue;
    yy1 = getSqrt(rem);
    if (yy1 == -1) continue;
    if (yy1 == yy3) continue;
    if (solve2(a, b) == true) {
      return true;
    }
  }
  return false;
}
int main() {
  cin >> a >> b;
  if (solve(a, b) == true || solve(b, a)) {
    cout << "YES\n";
    cout << xx1 << " " << yy1 << endl;
    cout << xx2 << " " << yy2 << endl;
    cout << xx3 << " " << yy3 << endl;
  } else {
    cout << "NO\n";
  }
  return 0;
}
