21274번 - Japanese Knowledge 다국어

This problem might be well-known in some countries, but how do other countries learn about such problems if nobody poses them?

You are given a non-decreasing positive integer sequence $A = (A_1, A_2, \ldots, A_N)$ of length $N$. For each $k=0,1,2,\ldots,N$, count the number of non-decreasing non-negative integer sequences $x = (x_1, x_2, \ldots, x_N)$ of length $N$ that satisfy following conditions, modulo $998244353$:

• $x_i \leq A_i$ for all $1 \leq i \leq N$.
• The number of indices $i$ with $x_i=A_i$ is exactly $k$.

The first line contains an integer $N$ ($1 \leq N \leq 250000$).

The second line contains $N$ integers $A_1,A_2,\ldots,A_N$ ($1 \leq A_1 \leq A_2 \leq \cdots \leq A_N \leq 250000$).

For each $k=0,1,2,\ldots,N$, print the answer.