CodeForces 658D Bear and Polynomials

题意：给一个多项式，然后告诉P(2)！=0，改变其中某一项的系数，使得P(2)=0，问你有多少种改变方法

思路：先正面扫一遍，把所有的系数都往后传，这样除了最后一个数的系数以外，其他的系数都是+-1,0这种然后我们再倒着扫一遍，判断这个数的系数应该是多少就好了。在从后面往前面走的过程中，如果某个位置的数大于了某个值的时候，就可以直接break了，因为会在不断的乘以2，不可能产生答案了。

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Description

Limak is a little polar bear. He doesn't have many toys and thus he often plays with polynomials.

He considers a polynomial valid if its degree is n and its coefficients are integers not exceeding k by the absolute value. More formally:

Let a₀, a₁, ..., a_n denote the coefficients, so . Then, a polynomial P(x) is valid if all the following conditions are satisfied:

• a_i is integer for every i;
• |a_i| ≤ k for every i;
• a_n ≠ 0.

Limak has recently got a valid polynomial P with coefficients a₀, a₁, a₂, ..., a_n. He noticed that P(2) ≠ 0 and he wants to change it. He is going to change one coefficient to get a valid polynomial Q of degree n that Q(2) = 0. Count the number of ways to do so. You should count two ways as a distinct if coefficients of target polynoms differ.

Input

The first line contains two integers n and k (1 ≤ n ≤ 200 000, 1 ≤ k ≤ 10⁹) — the degree of the polynomial and the limit for absolute values of coefficients.

The second line contains n + 1 integers a₀, a₁, ..., a_n (|a_i| ≤ k, a_n ≠ 0) — describing a valid polynomial . It's guaranteed that P(2) ≠ 0.

Output

Print the number of ways to change one coefficient to get a valid polynomial Q that Q(2) = 0.

Sample Input

Input

3 1000000000
10 -9 -3 5

Output

3

Input

3 12
10 -9 -3 5

Output

2

Input

2 20
14 -7 19

Output

0

转载于:https://www.cnblogs.com/q934098774/p/5388708.html