多项式 - 题目

#4314. 多项式

统计

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给定一个系数为 $\{0, 1\}$ 的多项式 $P$，输出其 $n$ 次幂中奇数系数的个数。

输入格式

第一行包含一个整数 $d$ ($1 \le d \le 20$)，表示多项式的次数。第二行包含 $d + 1$ 个整数 $a_i$ ($a_i \in \{0, 1\}$)，表示 $P$ 从低次到高次的系数。第三行包含一个整数 $n$ ($1 \le n \le 10^{16}$)。

输出格式

在唯一的一行中输出问题的答案。

样例

样例输入 1

1
1 1
3

样例输出 1

样例输入 2

5
0 1 1 0 1 1
3

样例输出 2

说明

在第一个样例测试中，$P(x)^3 = 1 + 3x + 3x^2 + x^3$，共有 4 个奇数系数。

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