D - Sum of Large Numbers

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 $(10^9+7)$.

3 2

10

The sum can take $10$ values, as follows:

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

200000 200001

1

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

141421 35623

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