Problem Statement

You are given an integer sequence $A = (A_0, A_1, \ldots, A_{2^N-1})$ of length $2^N$.

Additionally, $Q$ queries are given. For each $i = 1, 2, \ldots, Q$, the $i$-th query is represented by two integers $X_i$ and $Y_i$ and asks you to perform the operation below.

For each $j = 0, 1, 2, \ldots, 2^N-1$ in this order, do the following.

1. First, let $b_{N-1}b_{N-2}\ldots b_0$ be the binary representation of $j$ with $N$ digits. Additionally, let $j'$ be the integer represented by the binary representation $b_{N-1}b_{N-2}\ldots b_0$ after flipping the bit $b_{X_i}$ (changing $0$ to $1$ and $1$ to $0$).
2. Then, if $b_{X_i} = Y_i$, add the value of $A_j$ to $A_{j'}$.

Print each element of $A$, modulo $998244353$, after processing all the queries in the order they are given in the input.

What is binary representation with $N$ digits? The binary representation of an non-negative integer $X$ ($0 \leq X < 2^N$) with $N$ digits is the unique sequence $b_{N-1}b_{N-2}\ldots b_0$ of length $N$ consisting of $0$ and $1$ that satisfies: $\sum_{i = 0}^{N-1} b_i \cdot 2^i = X$.

Constraints

• $1 \leq N \leq 18$
• $1 \leq Q \leq 2 \times 10^5$
• $0 \leq A_i \lt 998244353$
• $0 \leq X_i \leq N-1$
• $Y_i \in \lbrace 0, 1\rbrace$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

N Q
A_0 A_1 \ldots A_{2^N-1}
X_1 Y_1
X_2 Y_2
\vdots
X_Q Y_Q

Output

For each $i = 0, 1, \ldots, 2^N-1$, print the remainder $A'_i$ when dividing $A_i$ after processing all the queries by $998244353$, separated by spaces, in the following format:

A'_0 A'_1 \ldots A'_{2^N-1}