## IE1 - Sweets

John has got *n* jars with candies. Each of the jars contains a different kind of candies (i.e. candies from the same jar are of the same kind, and candies from different jars are of different kinds). The *i*-th jar contains *m _{i}* candies. John has decided to eat some of his candies. He would like to eat at least

*a*of them but no more than

*b*. The problem is that John can't decide how many candies and of what kinds he would like to eat. In how many ways can he do it?

### Input

The first line of input contains three integers: *n*, *a* and *b*, separated by single spaces (1 ≤ *n* ≤ 10, 0 ≤ *a* ≤* b* ≤ 10000000). Each of the following *n* lines contains one integer. Line *i+1* contains integer *m _{i}* - the amount of candies in the

*i*-th jar (0 ≤

*m*≤ 1000000).

_{i}### Output

Let *k* be the number of different ways John can choose the candies to be eaten. The first and only line of output should contain one integer: *k* mod 2004 (i.e. the remainder of *k* divided by 2004).

### Example

Input:2 1 3 3 5Output:9`John can choose candies in the following ways: (1,0), (2,0), (3,0), (0,1), (0,2), (0,3), (1,1), (1,2), (2,1)`

Added by: | acheron |

Date: | 2013-10-19 |

Time limit: | 0.100s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ASM64 |

Resource: | CEOI 2004 |