Every $N$ Tarotian has a charisma value $a_i$. The Lover value of a line of $n$ ($n \ge 2$) Tarotians (represented by an array $a$), is defined as $$L(a) = \sum_{i=1}^{n-1}{a_i a_{i+1}}$$ For example, $$L([3, 5, 4, 6]) = a_1 a_2 + a_2 a_3 + a_3 a_4 = 15 + 20 + 24 = 59$$ You are given a number $A$, the well-known optimal Lover value. Determine whether the given line of Tarotians contains a sub-line of Tarotians of Lover value $A$. In other words, determine whether the given array contains a subarray of lover value $A$.

Input

The first line consists of two integers $N, A$. The second line consists of $N$ integers $a_i$.

Output

Output Yes or No.

Constraints

For all testcases: $1 \le N \le 10^6$, $-10^5 \le a_i \le 10^5$, $-10^{16} \le A \le 10^{16}$
Subtask 1 (20%): $N \le 10^3$
Subtask 2 (80%): No other constraints