9405: ABC207 —— E - Mod i
[Creator : ]
Description
Given is a sequence $A$ of $N$ numbers. Find the number of ways to separate $A$ into some number of non-empty contiguous subsequence $B_1, B_2, \ldots, B_k$ so that the following condition is satisfied:
- For every $i\ (1 \leq i \leq k)$, the sum of elements in $B_i$ is divisible by $i$.
Since the count can be enormous, print it modulo $(10^9+7)$.
- For every $i\ (1 \leq i \leq k)$, the sum of elements in $B_i$ is divisible by $i$.
Since the count can be enormous, print it modulo $(10^9+7)$.
Input
Input is given from Standard Input in the following format:
```
$N$
$A_1$ $A_2$ $\ldots$ $A_N$
```
```
$N$
$A_1$ $A_2$ $\ldots$ $A_N$
```
Output
Print the number of ways to separate the sequence so that the condition in the Problem Statement is satisfied, modulo $(10^9+7)$.
Constraints
- $1 \leq N \leq 3000$
- $1 \leq A_i \leq 10^{15}$
- All values in input are integers.
- $1 \leq A_i \leq 10^{15}$
- All values in input are integers.
Sample 1 Input
4
1 2 3 4
Sample 1 Output
3
We have three ways to separate the sequence, as follows:
- (1),(2),(3),(4)
- (1,2,3),(4)
- (1,2,3,4)
Sample 2 Input
5
8 6 3 3 3
Sample 2 Output
5
Sample 3 Input
10
791754273866483 706434917156797 714489398264550 918142301070506 559125109706263 694445720452148 648739025948445 869006293795825 718343486637033 934236559762733
Sample 3 Output
15