No.1929 Exponential Sequence
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問題文最終更新日: 2022-04-25 18:01:14
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Problem Statement
You are given an integer sequence $\{a_i \}$ of length $n$ and a positive integer $S$.
Count the integer sequences $\{k_i \}$ of length $n$ that satisfy the following conditions.
- $1 \le k_i$ for all $i$
- $\displaystyle\sum_{i=1}^{n} {a_i}^{k_i} \le S$
Constraints
- $1 \le n \le 8$
- $2 \le S, a_i \le 10^9$
- All inputs are integers.
Input
$n\ S$ $a_1\ a_2\ \dots a_n$
Output
Output the answer, followed by a newline.
Sample
Sample 1
Input
3 21 2 3 4
Output
7
Only $\{k_1, k_2, k_3\} = \{ 1, 1, 1 \}, \{ 1, 1, 2\}, \{ 1, 2, 1 \}, \{2, 1, 1\}, \{2, 2, 1 \}, \{3, 1, 1 \}, \{3, 2, 1 \}$ satisfy the conditions.
Sample 2
Input
4 124 13 133 1333 13333
Output
0
The answer may be $0$.
Sample 3
Input
5 1000000000 65536 2 37 382759279 15
Output
1009
Sample 4
Input
8 1000000000 2 2 2 2 2 2 2 2
Output
481891820460
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