Ex - Typical Convolution Problem

AtCoder

IDabc315_h

Time5000ms

Memory256MB

Difficulty—

You are given a sequence $(A_1, A_2, \ldots , A_N)$. Let us define a sequence $(F_0, F_1, \ldots , F_N)$ by the following formulae. * $F_0 = 1$ * $F_n = A_n\displaystyle\sum_{i+j<n}F_iF_j$ $(1 \leq n \leq N)$ Find $F_1, \ldots , F_N$ modulo $998244353$. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $0 \leq A_i < 998244353$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

5
1 2 3 4 5

Output #1

1 6 48 496 6240

$F_1 = A_1F_0F_0 = 1$. $F_2 = A_2(F_0F_0+F_0F_1+F_1F_0) = 6$. Similarly, we find $F_3 = 48, F_4 = 496, F_5 = 6240$.

Input #2

3
12345 678901 2345678

Output #2

12345 790834943 85679169

API Response (JSON)

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      "content": "You are given a sequence $(A_1, A_2, \\ldots , A_N)$. Let us define a sequence $(F_0, F_1, \\ldots , F_N)$ by the following formulae.\n\n*   $F_0 = 1$\n*   $F_n = A_n\\displaystyle\\sum_{i+j<n}F_iF_j$ $(1 \\l...",
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