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
import java.io.*;
import java.util.*;
 
 
 
public class Main {
	
	static InputReader in = new InputReader(System.in);
	static PrintWriter out = new PrintWriter(System.out);
	
	static int oo = (int)1e9;
//	static long oo = (long)1e15;
	static int mod = 1_000_000_007;
	
	static int[] di = {1, 0, 0, -1};
	static int[] dj = {0, -1, 1, 0};
	
	static long M = (long)1e17;
	static double EPS = 1e-13;
	
	
	
	public static void main(String[] args) throws IOException {

		int a = in.nextInt();
		int b = in.nextInt();
		
		for(int x = 1; x < a; ++x) {
			int yy = a * a - x * x;
			int y = (int)Math.round(Math.sqrt(yy));
			if(y * y == yy) {
				if(b * x % a == 0 && b * y % a == 0) {
					int x2 = -b * y / a;
					int y2 = b * x / a;
					if(y != y2) {
						System.out.println("YES");
						System.out.println(0 + " " + 0);
						System.out.println(x + " " + y);
						System.out.println(x2 + " " + y2);
						return;
					}
				}
			}
		}
		System.out.println("NO");
		
		out.close();
	}
	
	
	static int find(int[] g, int x) {
		return g[x] = g[x] == x ? x : find(g, g[x]);
	}
	
	static void union(int[] g, int[] size, int x, int y) {
		x = find(g, x); y = find(g, y);
		if(x == y)
			return;
		if(size[x] < size[y]) {
			g[x] = y;
			size[y] += size[x];
		}
		else {
			g[y] = x;
			size[x] += size[y];
		}
	}
	
	static class Segment {
		Segment left, right;
		long sum;
		long lazy;
		
		public Segment(long[] a, int l, int r) {
			super();
			if(l == r) {
				sum = a[l];
				return;
			}
			int mid = (l + r) / 2;
			left = new Segment(a, l, mid);
			right = new Segment(a, mid+1, r);
			sum = left.sum + right.sum;
		}
		
		boolean covered(int ll, int rr, int l, int r) {
			return ll <= l && rr >= r;
		}
		
		boolean noIntersection(int ll, int rr, int l, int r) {
			return ll > r || rr < l;
		}
		
		void lazyPropagation(int l, int r) {
			if(lazy != 0) {
				set(lazy, l, r); 
				if(left != null) {
					left.lazy += lazy;
					right.lazy += lazy;
				}
				lazy = 0;
			}
		}
		
		void set(long delta, int l, int r) {
			int sz = r - l + 1;
			sum += delta * sz; 
		}
		
		long query(int ll, int rr, int l, int r) {
			lazyPropagation(l, r);
			if(noIntersection(ll, rr, l, r))
				return 0;
			if(covered(ll, rr, l, r))
				return sum;
			int mid = (l + r) / 2;
			long leftSum = left.query(ll, rr, l, mid);
			long rightSum = right.query(ll, rr, mid+1, r);
			return leftSum + rightSum;
		}
		
//		int query(int k, int l, int r) {
//			Segment trace = this;
//			while(l < r) {
//				int mid = (l + r) / 2;
//				if(trace.left.size > k) {
//					trace = trace.left;
//					r = mid;
//				}
//				else {
//					k -= trace.left.size;
//					trace = trace.right;
//					l = mid + 1;
//				}
//			}
//			return trace.val;
//		}
		
		void update(int ll, int rr, long add, int l, int r) {
			lazyPropagation(l, r);
			if(noIntersection(ll, rr, l, r))
				return;
			if(covered(ll, rr, l, r)) {
				set(add, l, r);
				if(left != null) {
					left.lazy += add;
					right.lazy += add;
				}
				return;
			}
			int mid = (l + r) / 2;
			left.update(ll, rr, add, l, mid);
			right.update(ll, rr, add, mid+1, r);
			sum = left.sum + right.sum;
		}
	}
	
	static long pow(long a, long n, long mod) {
		if(n == 0)
			return 1;
		if(n % 2 == 1)
			return a * pow(a, n-1, mod) % mod;
		long x = pow(a, n / 2, mod);
		return x * x % mod;
	}
	
	
	static int[] getPi(char[] a) {
		int m = a.length;
		int j = 0;
		int[] pi = new int[m];
		for(int i = 1; i < m; ++i) {
			while(j > 0 && a[i] != a[j])
				j = pi[j-1];
			if(a[i] == a[j]) {
				pi[i] = j + 1;
				j++;
			}
		}
		return pi;
	}
	
	static long lcm(long a, long b) {
		return a * b / gcd(a, b);
	}
	
	static boolean nextPermutation(int[] a) {
		for(int i = a.length - 2; i >= 0; --i) {
			if(a[i] < a[i+1]) {
				for(int j = a.length - 1; ; --j) {
					if(a[i] < a[j]) {
						int t = a[i];
						a[i] = a[j];
						a[j] = t;
						for(i++, j = a.length - 1; i < j; ++i, --j) {
							t = a[i];
							a[i] = a[j];
							a[j] = t;
						}
						return true;
					}
				}
			}
		}
		return false;
	}
	
	static void shuffle(Object[] a) {
		Random r = new Random();
		for(int i = a.length - 1; i > 0; --i) {
			int si = r.nextInt(i);
			Object t = a[si];
			a[si] = a[i];
			a[i] = t;
		}
	}
	
	static void shuffle(int[] a) {
		Random r = new Random();
		for(int i = a.length - 1; i > 0; --i) {
			int si = r.nextInt(i);
			int t = a[si];
			a[si] = a[i];
			a[i] = t;
		}
	}
	
	static void shuffle(long[] a) {
		Random r = new Random();
		for(int i = a.length - 1; i > 0; --i) {
			int si = r.nextInt(i);
			long t = a[si];
			a[si] = a[i];
			a[i] = t;
		}
	}
	
	static int lower_bound(int[] a, int n, int k) {
		int s = 0;
		int e = n;
		int m;
		while (e - s > 0) {
			m = (s + e) / 2;
			if (a[m] < k)
				s = m + 1;
			else
				e = m;
		}
		return e;
	}
	static int lower_bound(long[] a, int n, long k) {
		int s = 0;
		int e = n;
		int m;
		while (e - s > 0) {
			m = (s + e) / 2;
			if (a[m] < k)
				s = m + 1;
			else
				e = m;
		}
		return e;
	}
	
	static int gcd(int a, int b) {
		return b == 0 ? a : gcd(b, a % b);
	}
	static long gcd(long a, long b) {
		return b == 0 ? a : gcd(b, a % b);
	}
	
	static class Pair implements Comparable<Pair> {
		int first, second;
 
		public Pair(int first, int second) {
			super();
			this.first = first;
			this.second = second;
		}
 
		@Override
		public int compareTo(Pair o) {
			return this.first != o.first ? this.first - o.first : this.second - o.second;
		}
		
//		@Override
//		public int compareTo(Pair o) {
//			return this.first != o.first ? o.first - this.first : o.second - this.second;
//		}
 
		@Override
		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + first;
			result = prime * result + second;
			return result;
		}
 
		@Override
		public boolean equals(Object obj) {
			if (this == obj)
				return true;
			if (obj == null)
				return false;
			if (getClass() != obj.getClass())
				return false;
			Pair other = (Pair) obj;
			if (first != other.first)
				return false;
			if (second != other.second)
				return false;
			return true;
		}
	}
}
 
 
 
class InputReader {
 
	private final InputStream stream;
	private final byte[] buf = new byte[8192];
	private int curChar, snumChars;
 
	public InputReader(InputStream st) {
		this.stream = st;
	}
 
	public int read() {
		if (snumChars == -1)
			throw new InputMismatchException();
		if (curChar >= snumChars) {
			curChar = 0;
			try {
				snumChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (snumChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}
 
	public int nextInt() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
 
	public long nextLong() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
 
	public int[] nextIntArray(int n) {
		int a[] = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = nextInt();
		}
		return a;
	}
 
	public String readString() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}
 
	public String nextLine() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}
 
	public boolean isSpaceChar(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}
 
	private boolean isEndOfLine(int c) {
		return c == '\n' || c == '\r' || c == -1;
	}
 
}