P6667 [Tsinghua Training 2016] How to Sum Elegantly

There is a polynomial function $f(x)$ whose highest power is $x^m$. Define a transformation $Q$: $$Q(f,n,x)=∑_{k=0}^{n}f(k)\binom nkx^k(1−x)^{n−k}$$ Now given $f$ and $n, x$, compute $Q(f,n,x)\bmod998244353$. For some reason, the function $f$ is given in point-value form. That is, $m+1$ numbers $a_0,a_1,⋯,a_m$ are given, and $f(x)=a_x$. It can be proven that this function is unique.

The first line contains three integers $n, m, x$, with meanings as described above. The second line contains $m+1$ integers, representing $a_0,a_1,⋯,a_m$.

Output one number in one line as the answer, taken modulo $998,244,353$.

#### Explanation for Sample $2$ After calculation, $f(x)=x^3$. #### Constraints For all testdata, it is guaranteed that $1≤n≤10^9$, $1≤m≤2×10^4$, and $0≤a_i,x