Mod i

AtCoder

IDabc207_e

Time2000ms

Memory256MB

Difficulty—

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 $(10^9+7)$. ## Constraints * $1 \leq N \leq 3000$ * $1 \leq A_i \leq 10^{15}$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

4
1 2 3 4

Output #1

3

We have three ways to separate the sequence, as follows:

*   $(1),(2),(3),(4)$
*   $(1,2,3),(4)$
*   $(1,2,3,4)$

Input #2

5
8 6 3 3 3

Output #2

Input #3

10
791754273866483 706434917156797 714489398264550 918142301070506 559125109706263 694445720452148 648739025948445 869006293795825 718343486637033 934236559762733

Output #3

15

The values in input may not fit into a $32$\-bit integer type.

API Response (JSON)

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      "content": "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 satisfie",
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      "memory_limit": 262144
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      "statement_type": "Markdown",
      "content": "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 satisfie...",
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