Nastya and a Game

## 题目描述 $Nastya$ 在生日那天收到了一个大小为 $n$ 的数组，她想知道数组存放的序列中，有多少的子串满足其中所有的数的乘积是数的总和的 $k$ 倍。请帮她得到答案。 ## 输入格式 第 $1$ 行，有 $2$ 个整数，分别表示数组的大小 $n$ 和倍数 $k$ 。 （数据范围： $1 \leqslant n \leqslant 2 \times 10^{5}$ ， $1 \leqslant k \leqslant 10^5$ ） 第 $2$ 行，有 $n$ 个整数，表示数组的元素 $a_i$ 。 （数据范围： $1 \leqslant a_i \leqslant 10^8$ ） ##输出格式 仅 $1$ 个整数，表示符合条件的子串数量。 ##提示与说明 - 第 $1$ 组样例的解释： 只有 $1$ 子串 $\{1\}$ ，因为 $\frac{1}{1}=k=1$ ，所以它恰好是符合条件的。 - 第 $2$ 组样例的解释： $\{6,\ 3\}$ 中所有数的乘积是 $18$ ，总和是 $9$ ，因为 $\frac{18}{9}=k=2$ ，所以它符合条件。 $\{3,\ 8,\ 1\}$ 中所有数的乘积是 $24$ ，总和是 $12$ ，因为 $\frac{24}{12} = k = 2$ ，所以它也符合条件。 综上所述，共有 $2$ 个子串符合条件。 感谢@Sooke 提供翻译以及@ZqlwMatt 修正

Nastya received one more array on her birthday, this array can be used to play a traditional Byteland game on it. However, to play the game the players should first select such a subsegment of the array that , where $ p $ is the product of all integers on the given array, $ s $ is their sum, and $ k $ is a given constant for all subsegments. Nastya wonders how many subsegments of the array fit the described conditions. A subsegment of an array is several consecutive integers of the array.

The first line contains two integers $ n $ and $ k $ ( $ 1<=n<=2·10^{5} $ , $ 1<=k<=10^{5} $ ), where $ n $ is the length of the array and $ k $ is the constant described above. The second line contains $ n $ integers $ a_{1},a_{2},...,a_{n} $ ( $ 1<=a_{i}<=10^{8} $ ) — the elements of the array.

In the only line print the number of subsegments such that the ratio between the product and the sum on them is equal to $ k $ .

1 1
1

1

4 2
6 3 8 1

2

In the first example the only subsegment is $ [1] $ . The sum equals $ 1 $ , the product equals $ 1 $ , so it suits us because . There are two suitable subsegments in the second example — $ [6,3] $ and $ [3,8,1] $ . Subsegment $ [6,3] $ has sum $ 9 $ and product $ 18 $ , so it suits us because . Subsegment $ [3,8,1] $ has sum $ 12 $ and product $ 24 $ , so it suits us because .