2.16([Usaco2005 Nov]Ant Counting)

describe

Bessie was poking around the ant hill one day watching the ants march to and fro while gathering food. She realized that many of the ants were siblings, indistinguishable from one another. She also realized the sometimes only one ant would go for food, sometimes a few, and sometimes all of them. This made for a large number of different sets of ants!

Being a bit mathematical, Bessie started wondering. Bessie noted that the hive has T (1 <= T <= 1,000) families of ants which she labeled 1..T (A ants altogether). Each family had some number Ni (1 <= Ni <= 100) of ants.

How many groups of sizes S, S+1, ..., B (1 <= S <= B <= A) can be formed?

While observing one group, the set of three ant families was seen as {1, 1, 2, 2, 3}, though rarely in that order. The possible sets of marching ants were:

3 sets with 1 ant: {1} {2} {3}
5 sets with 2 ants: {1,1} {1,2} {1,3} {2,2} {2,3}
5 sets with 3 ants: {1,1,2} {1,1,3} {1,2,2} {1,2,3} {2,2,3}
3 sets with 4 ants: {1,2,2,3} {1,1,2,2} {1,1,2,3}
1 set with 5 ants: {1,1,2,2,3}

Your job is to count the number of possible sets of ants given the data above.

Input

* Line 1: 4 space-separated integers: T, A, S, and B

* Lines 2..A+1: Each line contains a single integer that is an ant type present in the hive

Output

* Line 1: The number of sets of size S..B (inclusive) that can be created. A set like {1,2} is the same as the set {2,1} and should not be double-counted. Print only the LAST SIX DIGITS of this number, with no leading zeroes or spaces.

The sample input

3 5 2 3
1
2
2
1
3

Sample output

10

translate :

describe

One day , Bessie wandered around the ant hill , Watching the ants walk around while looking for food . She realized that many ants are brothers and sisters , There is no difference between them . She also realized that , Sometimes only one ant will go looking for food , Sometimes a few , Sometimes all the ants . This produces a large number of different kinds of ants !

Bessie is a bit mathematical , Start thinking . Bessie noticed that there were T (1 <= T <= 1000) A family of ants , She classified the ants as 1.T( It's all ants ). Each family has a number of Ni (1 <= Ni <= 100) The ants of .

How many group sizes are S S+1…, B (1 <= S <= B <= A) Can form ?

When observing a group , The collection of three ant families is regarded as {1,1,2,2,3}, Although rarely in this order . The possible assembly of marching ants is :

3 Group 1 An ant :{1}{2}{3}

5 Ants gather :{1,1}{1,2}{1,3}{2,2}{2,3}

5 Set 3 Ant :{1 1 2}{1 1 3}{1,2,2}{1,2,3}{2 2 3}

{1,1,2,2} {1,1,2,2} {1,1,2,3}

1 Group 5 Only ants :{1,1,2,2,3}

Your job is to calculate the number of possible ant colonies based on the above data .

Input

The first 1 That's ok :4 An integer separated by a space :T, A, S, B

The first 2 That's ok A+1: Each line contains a single integer , It is the type of ant that exists in the hive

Output

first line : The size that can be created is S..B( Include ) The number of sets . image {1,2} Such a set and {2,1} It's the same , Should not be double counted . Print only the last... Of the number 6 position , front 6 Bit cannot have 0 Or space .

The sample input

3 5 2 3
1
2
2
1
3

Sample output

10