Lower Algorithmics

Time limit4sMemory limit512 MB

Summary

Count the distinct positive integers that can be written as a sum of between l and r elements of set A, with repetition allowed.

Level: Medium7 of 10
Topics: Dynamic programming, Bit manipulation
Solved: No attempts yet

Problem

You are given a set $A$ of integers from $1$ to $1000$ inclusive. Your task is to find the number of positive integers that can be represented as a sum of several elements of $A$ , with number of summands being from $\ell$ to $r$ inclusive. Equal summands are allowed. Note that each number is counted only once, even if it has several such representations.

Input

The first line of the input contains three space-separated integers: $n$ , the number of elements in $A$ ( $1 \leq n \leq 1000$ ), followed by $\ell$ and $r$ , the bounds on number of summands ( $1 \leq \ell \leq r \leq 2000$ ). The second line contains $n$ space-separated integers $a\_1, a\_2, \ldots, a\_n$ ( $1 \leq a\_1 < a\_2 < \ldots < a\_n \leq 1000$ ): the elements of the set $A$ in increasing order.

Output

Output the number of integers that are representable as a sum of elements of $A$ , with number of summands being between $\ell$ and $r$ .

Examples3

Example 1
Input
```
2 1 2
1 2
```
Expected output
```
4
```
Example 2
Input
```
3 1 3
1 3 10
```
Expected output
```
18
```
Example 3
Input
```
6 3 5
1 2 3 4 5 6
```
Expected output
```
28
```