Contest Duration: - (local time) (100 minutes) Back to Home
D - Sum of Large Numbers /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

10^{100}, 10^{100}+1, ..., 10^{100}+NN+1 個の数があります。

この中から K 個以上の数を選ぶとき、その和としてあり得るものの個数を \bmod (10^9+7) で求めてください。

### 制約

• 1 \leq N \leq 2\times 10^5
• 1 \leq K \leq N+1
• 入力は全て整数

### 入力

N K


### 入力例 1

3 2


### 出力例 1

10


• (10^{100})+(10^{100}+1)=2\times 10^{100}+1
• (10^{100})+(10^{100}+2)=2\times 10^{100}+2
• (10^{100})+(10^{100}+3)=(10^{100}+1)+(10^{100}+2)=2\times 10^{100}+3
• (10^{100}+1)+(10^{100}+3)=2\times 10^{100}+4
• (10^{100}+2)+(10^{100}+3)=2\times 10^{100}+5
• (10^{100})+(10^{100}+1)+(10^{100}+2)=3\times 10^{100}+3
• (10^{100})+(10^{100}+1)+(10^{100}+3)=3\times 10^{100}+4
• (10^{100})+(10^{100}+2)+(10^{100}+3)=3\times 10^{100}+5
• (10^{100}+1)+(10^{100}+2)+(10^{100}+3)=3\times 10^{100}+6
• (10^{100})+(10^{100}+1)+(10^{100}+2)+(10^{100}+3)=4\times 10^{100}+6

### 入力例 2

200000 200001


### 出力例 2

1


### 入力例 3

141421 35623


### 出力例 3

220280457


Score : 400 points

### Problem Statement

We have N+1 integers: 10^{100}, 10^{100}+1, ..., 10^{100}+N.

We will choose K or more of these integers. Find the number of possible values of the sum of the chosen numbers, modulo (10^9+7).

### Constraints

• 1 \leq N \leq 2\times 10^5
• 1 \leq K \leq N+1
• All values in input are integers.

### Input

Input is given from Standard Input in the following format:

N K


### Output

Print the number of possible values of the sum, modulo (10^9+7).

### Sample Input 1

3 2


### Sample Output 1

10


The sum can take 10 values, as follows:

• (10^{100})+(10^{100}+1)=2\times 10^{100}+1
• (10^{100})+(10^{100}+2)=2\times 10^{100}+2
• (10^{100})+(10^{100}+3)=(10^{100}+1)+(10^{100}+2)=2\times 10^{100}+3
• (10^{100}+1)+(10^{100}+3)=2\times 10^{100}+4
• (10^{100}+2)+(10^{100}+3)=2\times 10^{100}+5
• (10^{100})+(10^{100}+1)+(10^{100}+2)=3\times 10^{100}+3
• (10^{100})+(10^{100}+1)+(10^{100}+3)=3\times 10^{100}+4
• (10^{100})+(10^{100}+2)+(10^{100}+3)=3\times 10^{100}+5
• (10^{100}+1)+(10^{100}+2)+(10^{100}+3)=3\times 10^{100}+6
• (10^{100})+(10^{100}+1)+(10^{100}+2)+(10^{100}+3)=4\times 10^{100}+6

### Sample Input 2

200000 200001


### Sample Output 2

1


We must choose all of the integers, so the sum can take just 1 value.

### Sample Input 3

141421 35623


### Sample Output 3

220280457