2019HUST_ACM邀请赛出题1

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Problem X Many Balls

Input file: standard input
Output file: standard output
Time limit: 1 seconds
Memory limit: 128MB

Description

You are given three integer numbers: $k$, $S(1\leq k,S \leq 10^{18})$ and a prime number $p(2\leq p \leq 5\times10^6)$,and we give $Ans$ a definition as following:
$Ans=\sum{\prod_{i=1}^{k}x_i}[x_i\geq1][\sum_{i=1}^kx_i\leq S]$
Assumed that $P$ is a proposition:
$[P]=\begin{cases} 1 & P=true \\ 0 & P =false \end{cases}$
Please output the $Ans$

Input

Three integer numbers: $k$, $S(1\leq k,S \leq 10^{18})$ and a prime number $p(2\leq p \leq 5\times10^6)$

Output

An integer $Ans$

Sample

Standard Input	Standard Output

2 4 37	15

Note

$x_1$	$x_2$	$x_1+x_2$	$x_1 \times x_2$
1	1	2	1
1	2	3	2
1	3	4	3
2	1	3	2
2	2	4	4
3	1	4	3

$Ans=(1 + 2 + 3 + 2 + 4 + 3)$ $mod$ $37$ $=15$