Problem:
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

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#pragma GCC optimize("Ofast,O3,unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma")

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <functional>
using namespace __gnu_pbds;
using namespace std;

#define endl '\n'
#define hoise cerr<<"hoise - "<<__LINE__<<"\n";
#define tham getchar();
#define FASTIO ios::sync_with_stdio(false);cin.tie(nullptr);

using ll = long long;
using ii = pair <int, int>;
using vi = vector <int>;
using vl = vector <ll>;

const int MXN = (int)2e5+6;
const double PI = acos(-1.0);
const ll mod = 1e9 + 7;

#define error(args...) { string _s = #args; replace(_s.begin(), _s.end(), ',', ' '); stringstream _ss(_s); istream_iterator<string> _it(_ss); err(_it, args); }
void err(istream_iterator<string> it) {}
template<typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
    cerr << *it << " = " << a << endl;
    err(++it, args...);
}

inline int Set(int N, int pos){return N=N | (1<<pos);}
inline int Reset(int N, int pos){return N=N & ~(1<<pos);}
inline bool Check(ll N, ll pos){return (bool)(N & (1LL<<pos));}

inline void normal(ll &a) { a %= mod; (a < 0) && (a += mod); }
inline ll modMul(ll a, ll b) { a %= mod, b %= mod; normal(a), normal(b); return (a * b) % mod; }
inline ll modAdd(ll a, ll b) { a %= mod, b %= mod; normal(a), normal(b); return (a + b) % mod; }
inline ll modSub(ll a, ll b) { a %= mod, b %= mod; normal(a), normal(b); a -= b; normal(a); return a; }
inline ll modPow(ll b, ll p) { ll r = 1; while (p) { if (p & 1) r = modMul(r, b); b = modMul(b, b); p >>= 1; } return r; }
inline ll modInverse(ll a) { return modPow(a, mod - 2); }
inline ll modDiv(ll a, ll b) { return modMul(a, modInverse(b)); }


template <typename T> using orderedSet = tree<T, null_type, greater<T>, rb_tree_tag, tree_order_statistics_node_update>;
template <typename T> using orderedSet1 = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
/*--------------------------------------------------------------------------------------------------------------------------*/




int main(){
	FASTIO
	
	int n, k;
	cin >> n >> k;
	
	ll sum[MXN + 4];
	
	for (int i = 1; i < MXN; ++i) {
		sum[i] = sum[i - 1] + i;
	}
	ll ans = 0;
	for (int i = k; i <= n + 1; ++i) {
		ll mnsum = sum[i];
		ll mxsum = sum[n + 1] - sum[n - i + 1];
		ans = ans + (mxsum - mnsum + 1) % mod;
		ans %= mod;
	}
	
	cout << ans % mod << endl;
	
    return 0;
}

/*

*/