F - Candy Retribution /

### 問題文

• L \leq A_1 + A_2 + ... + A_N \leq R
• N 個の要素を降順に並べたとき、上から M 番目と M+1 番目の要素は等しい。

### 制約

• 入力はすべて整数
• 1 \leq M < N \leq 3 \times 10^5
• 1 \leq L \leq R \leq 3 \times 10^5

### 入力

N M L R


### 入力例 1

4 2 3 7


### 出力例 1

105


\begin{eqnarray} &(1, 1, 1, 0), (1, 1, 1, 1), (2, 1, 1, 0), (2, 1, 1, 1), (2, 2, 2, 0), (2, 2, 2, 1), \\ &(3, 0, 0, 0), (3, 1, 1, 0), (3, 1, 1, 1), (3, 2, 2, 0), (4, 0, 0, 0), (4, 1, 1, 0), \\ &(4, 1, 1, 1), (5, 0, 0, 0), (5, 1, 1, 0), (6, 0, 0, 0), (7, 0, 0, 0)\end{eqnarray}

およびこれらの並べ替え，105 通りです。

### 入力例 2

2 1 4 8


### 出力例 2

3


### 入力例 3

141592 6535 89793 238462


### 出力例 3

933832916


Score: 1000 points

### Problem Statement

Find the number of sequences of N non-negative integers A_1, A_2, ..., A_N that satisfy the following conditions:

• L \leq A_1 + A_2 + ... + A_N \leq R
• When the N elements are sorted in non-increasing order, the M-th and (M+1)-th elements are equal.

Since the answer can be enormous, print it modulo 10^9+7.

### Constraints

• All values in input are integers.
• 1 \leq M < N \leq 3 \times 10^5
• 1 \leq L \leq R \leq 3 \times 10^5

### Input

Input is given from Standard Input in the following format:

N M L R


### Output

Print the number of sequences of N non-negative integers, modulo 10^9+7.

### Sample Input 1

4 2 3 7


### Sample Output 1

105


The sequences of non-negative integers that satisfy the conditions are:

\begin{eqnarray} &(1, 1, 1, 0), (1, 1, 1, 1), (2, 1, 1, 0), (2, 1, 1, 1), (2, 2, 2, 0), (2, 2, 2, 1), \\ &(3, 0, 0, 0), (3, 1, 1, 0), (3, 1, 1, 1), (3, 2, 2, 0), (4, 0, 0, 0), (4, 1, 1, 0), \\ &(4, 1, 1, 1), (5, 0, 0, 0), (5, 1, 1, 0), (6, 0, 0, 0), (7, 0, 0, 0)\end{eqnarray}

and their permutations, for a total of 105 sequences.

### Sample Input 2

2 1 4 8


### Sample Output 2

3


The three sequences that satisfy the conditions are (2, 2), (3, 3), and (4, 4).

### Sample Input 3

141592 6535 89793 238462


### Sample Output 3

933832916