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;
void err(istream_iterator<string> it) {}
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << "\n";
  err(++it, args...);
}
const double PI = acos(-1);
const double eps = (1e-9);
const long long int INF = 2e9;
const int M = (1e9) + 7;
const int N = 403;
struct Point {
  int x, y;
  Point(int a = 0, int b = 0) { x = a, y = b; }
  void reassign(int a, int b) { x = a, y = b; }
  void input() { scanf("%d%d", &x, &y); }
  void print() { printf("%d %d\n", x, y); }
  Point operator+=(Point A) {
    x += A.x, y += A.y;
    return *this;
  }
  Point operator-=(Point A) {
    x -= A.x, y -= A.y;
    return *this;
  }
  Point operator+(Point A) {
    Point tp(x + A.x, y + A.y);
    return tp;
  }
  Point operator-(Point A) {
    Point tp(x - A.x, y - A.y);
    return tp;
  }
  Point operator*(int f) {
    Point tp(x * f, y * f);
    return tp;
  }
  Point operator*=(int f) {
    x *= f, y *= f;
    return *this;
  }
  Point operator/=(int f) {
    x /= f, y /= f;
    return *this;
  }
  bool operator==(Point A) {
    if (x == A.x && y == A.y) return true;
    return false;
  }
  bool operator!=(Point A) {
    if (x != A.x || y != A.y) return true;
    return false;
  }
  void ulta() { swap(x, y); }
};
Point makepoint(int a, int b) {
  Point temp(a, b);
  return temp;
}
void swap(Point &A, Point &B) {
  swap(A.x, B.x);
  swap(A.y, B.y);
}
bool cmp(Point a, Point b) {
  if (a.x != b.x) return (a.x < b.x);
  return (a.y < b.y);
}
long long int dotproduct(Point a, Point b) {
  return (long long int)a.x * (long long int)b.x +
         (long long int)a.y * (long long int)b.y;
}
long long int crossproduct(Point a, Point b) {
  return (long long int)a.x * (long long int)b.y -
         (long long int)a.y * (long long int)b.x;
}
int ccw(Point a, Point b, Point origin = makepoint(0, 0)) {
  long long int x = crossproduct(a - origin, b - origin);
  if (x > 0) x = 1;
  if (x < 0) x = -1;
  return (int)x;
}
long long int sqrdist(Point a, Point b = makepoint(0, 0)) {
  long long int q = 0, temp;
  temp = a.x - b.x;
  temp *= temp, q += temp;
  temp = a.y - b.y;
  temp *= temp, q += temp;
  return q;
}
double dist(Point a, Point b = makepoint(0, 0)) {
  long long int temp = sqrdist(a, b);
  return sqrt(temp);
}
double anglepolar(Point a) { return atan2(a.y, a.x); }
double anglebetween(Point a, Point b, Point origin = makepoint(0, 0)) {
  return atan2(crossproduct(a - origin, b - origin),
               dotproduct(a - origin, b - origin));
}
Point perp(Point a) { return makepoint(-a.y, a.x); }
struct Line {
  Point a, b, ab;
  bool isline;
  Line() {
    a = makepoint(0, 0);
    b = a, ab = a, isline = 0;
  }
  Line(Point p, Point q) {
    a = p, b = q;
    ab = b - a;
    if (a != b)
      isline = 1;
    else
      isline = 0;
  }
  void update(Point p, Point q) {
    a = p, b = q;
    ab = b - a;
    if (a != b)
      isline = 1;
    else
      isline = 0;
    return;
  }
  bool operator==(Line other) {
    return ((crossproduct(ab, other.ab) == 0) && online(other.a));
  }
  bool online(Point point) {
    if (!isline) return (point == a);
    return (crossproduct(point - a, ab) == 0);
  }
  bool onsegment(Point point) {
    if (!isline) return (point == a);
    Point va, vb;
    va = a - point, vb = b - point;
    return (crossproduct(va, vb) == 0 && dotproduct(va, vb) <= 0);
  }
  bool parallel(Line other) { return (crossproduct(ab, other.ab) == 0); }
  bool perpendicular(Line other) { return (dotproduct(ab, other.ab) == 0); }
  double distline(Point point) {
    if (!isline) return dist(a, point);
    long double t = abs(crossproduct(point - a, ab));
    t /= dist(ab);
    return t;
  }
  double distsegment(Point point) {
    if (dotproduct(point - a, ab) <= 0) return dist(a, point);
    if (dotproduct(point - b, ab) >= 0) return dist(b, point);
    return distline(point);
  }
  bool lineintersectcheck(Line ray) { return (crossproduct(ab, ray.ab) != 0); }
  bool inter1(int a, int b, int c, int d) {
    if (a > b) swap(a, b);
    if (c > d) swap(c, d);
    return max(a, c) <= min(b, d);
  }
  bool segmentintersectcheck(Line ray) {
    if (crossproduct(ab, ray.ab) == 0) {
      if (online(ray.a))
        return inter1(a.x, b.x, ray.a.x, ray.b.x) &&
               inter1(a.y, b.y, ray.a.y, ray.b.y);
      return false;
    }
    return (crossproduct(ray.a - a, ray.a - b) !=
            crossproduct(ray.b - a, ray.b - b)) &&
           (crossproduct(a - ray.a, a - ray.b) !=
            crossproduct(b - ray.a, b - ray.b));
  }
};
int squarechecker(vector<Point> &point) {
  if (point[0] == point[2] || point[1] == point[3]) return 0;
  double x = dist(point[0], point[3]);
  if (dist(point[0], point[1]) == x && dist(point[1], point[2]) == x &&
      dist(point[2], point[3]) == x)
    return (dotproduct(point[1] - point[2], point[3] - point[2]) == 0);
  return 0;
}
vector<Point> v1;
vector<Point> v2;
void triplet(int x, vector<Point> &v) {
  int a, b;
  for (a = 1; a < x; ++a) {
    for (b = 1; b < x; ++b) {
      if (a * a + b * b == x * x) v.emplace_back(makepoint(a, b));
    }
  }
}
int main() {
  int i, j, n, m;
  scanf("%d%d", &n, &m);
  triplet(n, v1);
  triplet(m, v2);
  Point origin = makepoint(0, 0);
  Point p1, p2;
  for (i = 0; i < v1.size(); ++i) {
    for (j = 0; j < v2.size(); ++j) {
      p1 = v1[i], p2 = v2[j];
      if (p1.x > p1.y) p1.ulta();
      if (p2.x < p2.y) p2.ulta();
      if (p1.x * p2.x == p1.y * p2.y) {
        p1.x *= -1;
        if (p1.y == p2.y) p1.ulta(), p2.ulta(), p1 *= (-1);
        printf("YES\n");
        p1.print();
        p2.print();
        origin.print();
        exit(0);
      }
    }
  }
  printf("NO\n");
}
