You are given an integer $n$ and a sequence $a$ of $n-1$ integers, each element is either $0$ or $1$.

You are asked to build a string of length $n$ such that:

• each letter is one of "abcd";
• if $a_i=1$, then the $i$-th suffix of the string is lexicographically smaller than the $(i+1)$-th suffix;
• if $a_i=0$, then the $i$-th suffix of the string is lexicographically greater than the $(i+1)$-th suffix.

You will be asked $q$ queries of form:

• $i$ ($1 \le i \le n - 1$) — flip the value of $a_i$ (if $a_i=0$, then set $a_i$ to $1$, and vice versa).

After each query print the number of different strings that satisfy the given constraints modulo $998\,244\,353$.

The first line contains two integers $n$ and $q$ ($2 \le n \le 10^5$; $1 \le q \le 10^5$) — the length of the string and the number of queries.

The second line contains $n-1$ integers $a_1, a_2, \dots, a_{n-1}$ ($a_i \in \{0, 1\}$) — the constraints on suffixes of the string.

Each of the next $q$ lines contains a query: an integer $i$ ($1 \le i \le n - 1$) — flip the value of $a_i$ (if $a_i=0$, then set $a_i$ to $1$, and vice versa).

After each query print the number of different strings that satisfy the given constraints modulo $998\,244\,353$.