Prefix Sum Transformation

In this problem, you are given an integer n, an integer a, and an array f of size n+1 (with indices from 0 to n). Initially, the array f represents the coefficients of a polynomial

$$F(x)=\sum_{i=0}^{n} f_i\,x^i.$$

You perform the following transformation exactly n times:

$$\text{For } t=1,2,\dots,n:\quad \forall\, 1\le i\le n,\quad f_i \leftarrow f_i + a\,f_{i-1}. $$

After the t-th transformation, the answer ans[t] is defined as the updated value of f[t]. It can be shown that after t transformations the new polynomial is

$$F_t(x)=F(x)\,(1+a\,x)^t.$$

Thus, we have

$$\displaystyle \text{ans}_t = \sum_{j=0}^{t}\binom{t}{j} a^{j}\,f_{t-j} \quad\text{for}\; t=1,2,\dots,n. $$

Since the numbers can be very large, output each ans_t modulo 998244353.

inputFormat

The first line contains two integers n and a.

The second line contains n+1 integers: f[0], f[1], \dots, f[n].

outputFormat

Output n integers: ans[1], ans[2], \dots, ans[n] where each number is taken modulo 998244353.

sample

3 2
1 2 3 4

4 15 54