100 years have passed since the last victory of the man versus computer in Go. Technologies made a huge step forward and robots conquered the Earth! It's time for the final fight between human and robot that will decide the faith of the planet.

The following game was chosen for the fights: initially there is a polynomial P(x) = a_{n}x^{n} + a_{n} - 1x^{n} - 1 + ... + a_1x + a_0,  with yet undefined coefficients and the integer k. Players alternate their turns. At each turn, a player pick some index j, such that coefficient a_{j} that stay near x^{j} is not determined yet and sets it to any value (integer or real, positive or negative, 0 is also allowed). Computer moves first. The human will be declared the winner if and only if the resulting polynomial will be divisible by Q(x) = x - k.

Polynomial P(x) is said to be divisible by polynomial Q(x) if there exists a representation P(x) = B(x)Q(x), where B(x) is also some polynomial.

Some moves have been made already and now you wonder, is it true that human can guarantee the victory if he plays optimally?


-----Input-----

The first line of the input contains two integers n and k (1 ≤ n ≤ 100 000, |k| ≤ 10 000) — the size of the polynomial and the integer k.

The i-th of the following n + 1 lines contain character '?' if the coefficient near x^{i} - 1 is yet undefined or the integer value a_{i}, if the coefficient is already known ( - 10 000 ≤ a_{i} ≤ 10 000). Each of integers a_{i} (and even a_{n}) may be equal to 0.

Please note, that it's not guaranteed that you are given the position of the game where it's computer's turn to move.


-----Output-----

Print "Yes" (without quotes) if the human has winning strategy, or "No" (without quotes) otherwise.


-----Examples-----
Input
1 2
-1
?

Output
Yes

Input
2 100
-10000
0
1

Output
Yes
Input
4 5
?
1
?
1
?

Output
No


-----Note-----

In the first sample, computer set a_0 to  - 1 on the first move, so if human can set coefficient a_1 to 0.5 and win.

In the second sample, all coefficients are already set and the resulting polynomial is divisible by x - 100, so the human has won.

Difficulty: interview

Starter code:

Solutions:
p=1048583
q=1048589
modd=p*q*p*q
n,k=tuple(map(int,input().split()))
a=[0]
wenhao=0
gai=0
for i in range(n+1):
    m=input()
    if m[0]=='?':
        a.append('?')
        wenhao+=1
    else:
        a.append(int(m))
        gai+=1

if k==0:
    if (a[1]=='?' and gai&1==1) or a[1]==0:
        print('Yes')
    else:
        print('No')
else:
    if wenhao!=0:
        if n&1==1:
            print('Yes')
        else:
            print('No')
    else:
        m=a[n+1]
        nn=a[n]
        for i in range(n,0,-1):
            m,nn=(nn+k*m)%modd,a[i-1]
        if m==0:
            print('Yes')
        else:
            print('No')


n, k = map(int, input().split())
a = []

check = 0
for _ in range(n + 1):
	new_a = input()
	if new_a == '?':
		check += 1
	else:
		new_a = int(new_a)

	a.append(new_a)

if check > 0:
	if k != 0:
		if (n + 1) % 2 == 0:
			print('Yes')
		else:
			print('No')
	else:
		if ((n + 1 - check) % 2 == 1 and a[0] == '?') or a[0] == 0:
			print('Yes')
		else:
			print('No') 
else:
	module1 = 2**58 - 203
	module2 = 2**64 - 59
	result1 = result2 = result3 = 0
	for c in a[::-1]:
		result1 = (result1 * k + c) % module1
		result2 = (result2 * k + c) % module2
		result3 = (result3 * k + c) % (module1 + module2)

	if result1 == 0 and result2 == 0 and result3 == 0:
		print('Yes')
	else:
		print('No')

n,k = [int(x) for x in input().split()]
L=[]
done = 0
for i in range(n+1):
    c=input()
    if c is '?':
        L.append('?')
    else:
        L.append(int(c))
        done += 1

left = n + 1 - done

if done%2 == 0:
    chance = 0
else:
    chance = 1

if k==0:
    if L[0] is '?':
        print('Yes' if chance == 1 else 'No')
    else:
        print('Yes' if L[0] == 0 else 'No')
elif left == 0:
    for i in range(n, 0,-1):
        L[i-1] += L[i]*k
        if not (-10000000000<L[i-1]<10000000000):
            L[0]=-1
            break
    print('Yes' if L[0] == 0 else 'No')
elif left%2 == 0:
    if chance == 0:
        print('Yes')
    else:
        print('No')
else:
    if chance == 1:
        print('Yes')
    else:
        print('No')
        
    



import sys
#sys.stdin=open("data.txt")
input=sys.stdin.readline

n,k=map(int,input().split())

coeff=[str(input().strip()) for _ in range(n+1)]

if coeff.count('?')==0:
    # check game state
    total=0
    for s in range(n+1)[::-1]:
        total=total*k+int(coeff[s])
        if abs(total)>1000000000000: break
    if total==0: print("Yes")
    else: print("No")
elif k==0:
    if coeff[0]=='?':
        # check if human's turn
        if (n+1-coeff.count('?'))%2==1: print("Yes")
        else: print("No")
    else:
        if coeff[0]=='0': print("Yes")
        else: print("No")
else:
    # k is not 0
    # check if human moves last
    if (n+1)%2==0: print("Yes")
    else: print("No")

def solve():
	modx = 179426080107
	n,m = list(map(int,input().split()))
	cnt = 0
	a = []
	for i in range(n + 1):
		s = input()
		if(s == '?'): cnt += 1
		a.append(s)

	#print(cnt)

	if (m == 0):
		if (a[0] == '0') : return 1
		if (a[0] == '?' and (n + 1 - cnt)% 2 == 1):
			return 1
		return 0

	if(cnt):
		if (n % 2 == 1):return 1
		return 0

	for i in range(n+1):
		a[i] = int(a[i])

	now = a[n]

	tmp = 1
	ans = 0
	for i in range(n + 1):
		ans = ans + (tmp * a[i]) % modx
		ans %= modx
		tmp = (tmp * m) % modx

	if (ans == 0) : return 1
	else : return 0

if (solve() == 1) : print("Yes")
else : print("No")





n,k = map(int,input().split())
s = 0
a = 0
l = []
f = False
for i in range(n+1):
    v = input()
    if v == '?':
        a += 1
        if k == 0 and i == 0:
            f = True
    elif a==0:
        l.append(int(v))
l.reverse()
if a == 0 and k != 0:
    for i in l:
        s = k*s + i
        if s > 10**18 or s < -10**18:
            break
if k == 0 and ((not f and l[-1] == 0) or (f and (n-a)%2==0)):
    print("Yes")
elif k == 0:
    print("No")
elif (a == 0 and s == 0) or (n%2 == 1 and a > 0):
    print("Yes")
else:
    print("No")

n,k = map(int,input().split())
s = 0
a = 0
l = []
f = False
for i in range(n+1):
    v = input()
    if v == '?':
        a += 1
        if k == 0 and i == 0:
            f = True
    elif a==0:
        l.append(int(v))
l.reverse()
if a == 0 and k != 0:
    for i in l:
        s = k*s + i
        if s > 10**9 or s < -10**9:
            break
if k == 0 and ((not f and l[-1] == 0) or (f and (n-a)%2==0)):
    print("Yes")
elif k == 0:
    print("No")
elif (a == 0 and s == 0) or (n%2 == 1 and a > 0):
    print("Yes")
else:
    print("No")

n, k = map(int,input().split())
a = []
for i in range(n+1):
    a.extend(input().split())
if k == 0:
    if a[0] == '0': print('Yes')
    
    elif a[0] == '?' and (n - a.count('?'))% 2 == 0: print('Yes')
    else: print('No')
elif '?' in a:
    if n % 2 == 0: print('No')
    else: print('Yes')
else:
    a = list(map(int, a))[::-1]
    res = a[0]
    for i in range(1, n+1):
        res = a[i] + res * k
        if res > 10**11 or res < -10**11: 
            print('No')
            return
    if res == 0: print('Yes')
    else: print('No')

n, k = map(int, input().split())
a = [input() for i in range(n + 1)]
z = 0
for i in a:
    if i == '?':
        z += 1
if k == 0:
    if a[0] == '0': 
        print('Yes')
    elif a[0] == '?' and (n - z + 1) % 2 == 1:
        print('Yes')
    else:
        print('No')
else:
    if z == 0:
        d = 0
        for i in a[::-1]:
            d = (d * k + int(i)) % 7272763523821
            #print(d)
        if d == 0:
            print('Yes')
        else:
            print('No')
    else:
        if n % 2 == 0:
            print('No')
        else:
            print('Yes')

n, k = list(map(int, input().split()))
a = [input() for _ in range(n + 1)]
c = len([_ for _ in a if _ == '?'])
print('Yes' if k == 0 and (a[0] == '0' or a[0] == '?' and (n + 1 - c) % 2 == 1) or k != 0 and (c > 0 and n % 2 == 1 or c == 0 and sum([_ * pow(k, i, 10**15 + 91) for i, _ in enumerate(map(int, a))]) % (10**15 + 91) == 0) else 'No')


n,k = map(int,input().split(" "))
mas=[-100000000000000]*(n+1)
d = 0
limit = 10**10
for i in range(n+1):
    s= input()
    if s=="?":
        d+=1
    else:
        mas[i]=int(s)
if k == 0 and mas[0] == 0:
    print("Yes")
elif k == 0 and mas[0] != 0 :
    if mas[0]==-100000000000000:
        if (n-d)%2!=0:
            print("No")
        else:
            print("Yes")
    else:
        print("No")
else:
    if d!=0:
        if n%2==0:
            print("No")
        else:
            print("Yes")
    else:

        b=mas[n]
        for i in range(n-1,0,-1):
            b=(mas[i]+b*k)
            if abs(b)>limit:
                print("No")
                break
        else:
            print("Yes") if (b*k==-mas[0]) else print("No")


def main():
    n, k = list(map(int, input().split()))
    aa = []
    for i in range(n + 1):
        s = input()
        aa.append(None if s == '?' else int(s))
    qm_cnt = aa.count(None)
    if k:
        if qm_cnt:
            print('Yes' if n & 1 else 'No')
        else:
            x = 0
            for a in reversed(aa):
                x = (x * k + a) % 999999937
            print('No' if x else 'Yes')
    else:
        print('Yes' if aa[0] is None and not (n - qm_cnt) & 1 or aa[0] == 0 else 'No')


def __starting_point():
    main()

__starting_point()

import sys
import math

def calculate(A, k, x):
    res = 0
    if abs(k) >= 2:
        for a in reversed(A):
            res = k*res + a
            if abs(res) > x:
                return float('inf')
        return res
    else:
        for a in reversed(A):
            res = k*res + a
        return res

def solve():
    n, k = [int(x) for x in input().split()]
    A = ['?' if line == '?\n' else int(line) for line in sys.stdin]

    if k == 0:
        return A[0] == 0 or A[0] == '?' and (n + 1 - A.count('?')) % 2 == 1
    else:
        if '?' in A:
            return n % 2 == 1
        else:
            return calculate(A, k, 10000) == 0

print('Yes' if solve() else 'No')