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).

Examples

Input

3 2

Output

10

Input

200000 200001

Output

1

Input

141421 35623

Output

220280457

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见题面