407_A. Triangle
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
```python
import os
import sys
from io import BytesIO, IOBase


def main():
    pass


# region fastio

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
def count1(s):
    c=0
    for i in s:
        if(i=='1'):
            c+=1
    return(c)
def binary(n):
    return(bin(n).replace("0b",""))
def decimal(s):
    return(int(s,2))
def pow2(n):
    p=0
    while(n>1):
        n//=2
        p+=1
    return(p)
def isPrime(n):
    if(n==1):
        return(False)
    else:
        root=int(n**0.5)
        root+=1
        for i in range(2,root):
            if(n%i==0):
                return(False)
        return(True)
a,b=map(int,input().split())
a,b=min(a,b),max(a,b)
f=False
ans=[[0,0]]
f=False
l1=[]
l2=[]
for i in range(1,a):
    t=(a*a-i*i)**0.5
    if(int(t)==t):
        l1.append([int(t),i])
for i in range(1,b):
    t=(b*b-i*i)**0.5
    if(int(t)==t):
        l2.append([int(t),-i])
f=True
for i in range(0,len(l1)):
    if(f):
        for j in range(0,len(l2)):
            x1=l1[i][0]
            x2=l2[j][0]
            y1=l1[i][1]
            y2=l2[j][1]
            if(x1!=x2 and ((y2-y1)**2+(x2-x1)**2)==(a**2+b**2)):
                f=False
                print("YES")
                print(0,0)
                print(x1,y1)
                print(x2,y2)
                break
if(f):
    print("NO")
```