|Codeforces Round #354 (Div. 2)|
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
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?
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 xi - 1 is yet undefined or the integer value ai, if the coefficient is already known ( - 10 000 ≤ ai ≤ 10 000). Each of integers ai (and even an) 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.
Print "Yes" (without quotes) if the human has winning strategy, or "No" (without quotes) otherwise.
In the first sample, computer set a0 to - 1 on the first move, so if human can set coefficient a1 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.