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)

#ifdef Nyan_Nyan
#pragma region template
#endif

#include <bits/stdc++.h>

#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define sz(a) (ll)(a).size()
#define last(a) (a).at((ll)(a).size()-1)
#define rep(i,n) for(ll i=0,i##_len=(n);i<i##_len;i++)
#define brep(i,a,b) for(ll i=(a),i##_len=(b);i<=i##_len;i++)
#define rrep(i,n) ll i=(n);ll now=-1;while(i--&&(now++||1))
#define xrep(i,n) for(ll i=1,i##_len=(n);i<=i##_len;i++)
#define Yes(n) cout<<((n)?YES:NO)<<'\n'
#define co(n) cout<<(n)<<'\n'
#define Sort(v) sort(all(v))
#define rSort(v) sort(all(v),greater<typeof(v[0])>())
#define Rev(v) reverse(all(v))
#define Unique(v) (v).erase(unique(all(v)),(v).end())
#define eb emplace_back
#define fi first
#define se second

#ifdef ONLINE_JUDGE
#define comment(msg)
#define local(x)
#define debug(x,y) y
#else
#define comment(msg) cout << "{ " << msg << " }\n"
#define local(x) x
#define debug(x,y) x
#endif

template <uint_fast64_t Modulus> class modint {
  using u64 = uint_fast64_t;

public:
  u64 a;

  constexpr modint(const u64 x = 0) noexcept : a(x % Modulus) {}
  constexpr u64 &value() noexcept { return a; }
  constexpr const u64 &value() const noexcept { return a; }
  constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint &operator+=(const modint rhs) noexcept {
    a += rhs.a;
    if (a >= Modulus) {
      a -= Modulus;
    }
    return *this;
  }
  constexpr modint &operator-=(const modint rhs) noexcept {
    if (a < rhs.a) {
      a += Modulus;
    }
    a -= rhs.a;
    return *this;
  }
  constexpr modint &operator*=(const modint rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    u64 exp = Modulus - 2;
    while (exp) {
      if (exp % 2) {
        *this *= rhs;
      }
      rhs *= rhs;
      exp /= 2;
    }
    return *this;
  }
};

std::istream& operator>>(std::istream& is, const modint<1000000007>& x) { return is >> x.a; }
std::ostream& operator<<(std::ostream& os, const modint<1000000007>& x) { return os << x.a; }

using namespace std;
using ll = long long;
using vll = vector<ll>;
using vbl = vector<bool>;
using vint = vector<int>;
using vvll = vector<vll>;
using vvbl = vector<vbl>;
using vdbl = vector<double>;
using vstr = vector<string>;
using vvint = vector<vint>;
using mint = modint<1000000007>;

constexpr int INF = 1e9;
constexpr ll LINF = 1e18;
constexpr ll MAX = 1e6;
constexpr ll MOD = 1000000007;

// --- functions which take 1 argument --- //
static inline void ignore_ret(int x){x++;}
template<class T> inline int sgn(T x){return (x>0)-(x<0);}
template<class T> inline double rad_to_deg(T a){return a/180.0*M_PI;}
template<class T> inline double deg_to_rad(T a){return a/M_PI*180.0;}
template<class T> inline ll factorial(T n){if(n==0)return 1;ll r=1;for(T i=2;i<=n;i++)r*=i;return r;}
template<class T> inline map<T,T> factorize(T n){map<T,T>r;for(T i=2;i*i<=n;i++){while(n%i==0){r[i]++;n/=i;}}if(n!=1)r[n]=1;return r;}
template<class T> inline vector<T> divisor(T n){vector<T>r;for(T i=1;i*i<=n;i++){if(!(n%i)){r.eb(i);if(i*i!=n)r.eb(n/i);}}Sort(r);return r;}

// --- functions which take 2 arguments --- //
template<class T> inline bool chmax(T&a,const T&b){if(a<b){a=b;return 1;}return 0;}
template<class T> inline bool chmin(T&a,const T&b){if(a>b){a=b;return 1;}return 0;}
template<class T> inline T nPr(T n,T k){if(n<k||n<0||k<0)return 0;T r=1;for(T i=n-k+1;i<=n;i++)r*=i;return r;}
template<class T> inline T nCr(T n,T k){if(n<k||n<0||k<0)return 0;T r=1;k=min(k,n-k);for(T i=n-k+1;i<=n;i++)r*=i;return r/factorial(k);}

// --- functions which take vector(s) as argument(s) --- //
template<class T> inline void print(T v){cout<<"[ ";for(auto x:v)cout<<x<<' ';cout<<"]\n";}
template<class T> inline void print_2d(vector<T>v){for(T x:v)print<T>(x);}
template<class T> inline void print_d(T v,string d){rep(i,sz(v)-1)cout<<v[i]<<d;cout<<last(v)<<'\n';}
template<class T> inline void print_2d_d(vector<T>v,string d){for(T x:v)print_d<T>(x,d);}
template<class T> inline T min(vector<T>v){return *min_element(all(v));}
template<class T> inline T max(vector<T>v){return *max_element(all(v));}
template<class T> inline ll sum(T v){return reduce(all(v),0LL);}
template<class T> inline T gcd(vector<T>v){T r=v[0];brep(i,1,sz(v)-1)r=gcd(r,v[i]);return r;}
template<class T> inline T lcm(vector<T>v){T r=v[0];brep(i,1,sz(v)-1)r=lcm(r,v[i]);return r;}
template<class T> inline double abs(vector<T>v){return sqrt(reduce(all(v),0.0,[](T s,T v){return s+=v*v;}));}
template<class T> inline T vector_add(T u,T v){T r;rep(i,u.size())r.eb(u[i]+v[i]);return r;}
template<class T> inline T vector_subtract(T u,T v){T r;rep(i,u.size())r.eb(u[i]-v[i]);return r;}
template<class T> inline T dot_product(vector<T>u,vector<T>v){if(u.size()<v.size())return 0;T r=0;for(ll i=0;i<u.size();i++)r+=u[i]*v[i];return r;}
template<class T> inline T cross_product(T u,T v){T r(3);r[0]=u[1]*v[2]-u[2]*v[1];r[1]=u[2]*v[0]-u[0]*v[2];r[2]=u[0]*v[1]-u[1]*v[0];return r;}

// --- functions which take set as argument --- //
template<class T> inline T min(set<T>v){return *min_element(all(v));}
template<class T> inline T max(set<T>v){return *max_element(all(v));}
template<class T> inline T gcd(set<T>v){T r=0;for(T x:v)r=(r==0)?x:gcd(r,x);return r;}
template<class T> inline T lcm(set<T>v){T r=0;for(T x:v)r=(r==0)?x:lcm(r,x);return r;}
template<class T> inline T min(unordered_set<T>v){return *min_element(all(v));}
template<class T> inline T max(unordered_set<T>v){return *max_element(all(v));}
template<class T> inline T gcd(unordered_set<T>v){T r=0;for(T x:v)r=(r==0)?x:gcd(r,x);return r;}
template<class T> inline T lcm(unordered_set<T>v){T r=0;for(T x:v)r=(r==0)?x:lcm(r,x);return r;}

#ifdef Nyan_Nyan
#pragma endregion template
#endif
// option: mod

ll N, K;
mint ans;

ll calc(ll i) {
  ll smallest = i * (i-1) / 2;
  ll largest = smallest + i * (N - i + 1);
  return largest - smallest + 1;
}

void solve(ll N, ll K) {
  for (ll i = K; i <= N+1; i++) {
    ans += calc(i);
  }
  co(ans);
}

int main() {
  ignore_ret(scanf("%lld",&N));
  ignore_ret(scanf("%lld",&K));
  solve(N, K);
  return 0;
}