This documentation is automatically generated by online-judge-tools/verification-helper
This project is maintained by tsutaj
#include <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>
using namespace std;
#include "../math_017_modint.cpp"
#include "../math_015_remainder_sum.cpp"
// Verified on Mar 30, 2019
// Educational Codeforces Round 5 E: Sum of Remainders
// Judge: https://codeforces.com/contest/616/problem/E
void ECR005_E() {
long long int N, M; cin >> N >> M;
using mint = ModInt<1000000007>;
RemainderSum<mint> rs(N);
cout << rs.sum_func(M) << endl;
}
// Verified on Mar 30, 2019
// yukicoder No. 752: mod 数列
// Judge: https://yukicoder.me/problems/no/752
void yuki_752() {
long long int P, Q; cin >> P >> Q;
RemainderSum<long long int> rs(P);
while(Q--) {
long long int l, r; cin >> l >> r;
cout << rs.sum_func(l, r) << endl;
}
}
int main() {
ECR005_E();
// yuki_752();
return 0;
}
#line 1 "math/verify/verify_math_015_remainder_sum.cpp"
#include <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>
using namespace std;
#line 1 "math/math_017_modint.cpp"
// ModInt begin
using ll = long long;
template<ll mod>
struct ModInt {
ll v;
ll mod_pow(ll x, ll n) const {
return (!n) ? 1 : (mod_pow((x*x)%mod,n/2) * ((n&1)?x:1)) % mod;
}
ModInt(ll a = 0) : v((a %= mod) < 0 ? a + mod : a) {}
ModInt operator+ ( const ModInt& b ) const {
return (v + b.v >= mod ? ModInt(v + b.v - mod) : ModInt(v + b.v));
}
ModInt operator- () const {
return ModInt(-v);
}
ModInt operator- ( const ModInt& b ) const {
return (v - b.v < 0 ? ModInt(v - b.v + mod) : ModInt(v - b.v));
}
ModInt operator* ( const ModInt& b ) const {return (v * b.v) % mod;}
ModInt operator/ ( const ModInt& b ) const {return (v * mod_pow(b.v, mod-2)) % mod;}
bool operator== ( const ModInt &b ) const {return v == b.v;}
bool operator!= ( const ModInt &b ) const {return !(*this == b); }
ModInt& operator+= ( const ModInt &b ) {
v += b.v;
if(v >= mod) v -= mod;
return *this;
}
ModInt& operator-= ( const ModInt &b ) {
v -= b.v;
if(v < 0) v += mod;
return *this;
}
ModInt& operator*= ( const ModInt &b ) {
(v *= b.v) %= mod;
return *this;
}
ModInt& operator/= ( const ModInt &b ) {
(v *= mod_pow(b.v, mod-2)) %= mod;
return *this;
}
ModInt pow(ll x) { return ModInt(mod_pow(v, x)); }
// operator int() const { return int(v); }
// operator long long int() const { return v; }
};
template<ll mod>
ModInt<mod> pow(ModInt<mod> n, ll k) {
return ModInt<mod>(n.mod_pow(n.v, k));
}
template<ll mod>
ostream& operator<< (ostream& out, ModInt<mod> a) {return out << a.v;}
template<ll mod>
istream& operator>> (istream& in, ModInt<mod>& a) {
in >> a.v;
return in;
}
// ModInt end
#line 1 "math/math_015_remainder_sum.cpp"
// F(i) := P (mod 1) + P (mod 2) + ... + P (mod i) を計算
// 答えは NumType 型で返ってくる
template <typename NumType, int K = 10000000>
struct RemainderSum {
using lint = long long;
lint P;
vector<NumType> small_case;
RemainderSum(lint P_) {
P = P_;
build();
}
// 小さいケースに対する答えを覚える
void build() {
small_case.resize(K + 1, NumType(0));
for(lint i=1; i<=K; i++) {
NumType mod(P % i);
small_case[i] = small_case[i-1] + mod;
}
}
// [1, x] (閉区間であることに注意!!)
// F(x) を計算
NumType sum_func(lint x) {
if(x <= K) return small_case[x];
return small_case[K] + sum_func(K+1, x);
}
// [l, r] (閉区間であることに注意!!)
// P (mod l) + P (mod l+1) + ... + P (mod r) を計算
NumType sum_func(lint l, lint r) {
if(r <= K) return small_case[r] - small_case[l-1];
if(l <= K) return small_case[K] - small_case[l-1] + sum_func(K+1, r);
NumType ans(0);
// l も r も、 K を超える値である
lint dmax = P / l, dmin = P / r, num = l;
for(lint div=dmax; div>=dmin; div--) {
if(div == 0) {
// 商が div になるような要素のインデックス (閉区間)
lint idx_l = max(l, P + 1);
lint idx_r = r;
NumType range(idx_r - idx_l + 1);
// このときの剰余の値は全て P に等しい
NumType sum = range * NumType(P);
ans += sum;
}
else {
// 商が div になるような要素のインデックス (閉区間)
lint idx_l = max(l, P / (div + 1) + 1);
lint idx_r = min(r, P / div);
NumType range(idx_r - idx_l + 1);
// 左端と右端について、その剰余の値
NumType mod_l(P % idx_l);
NumType mod_r(P % idx_r);
// 等差数列の和
NumType sum = range * (mod_l + mod_r) / NumType(2);
ans += sum;
// 次の div を求める (1 ずつ減らない場合がある)
if(P / num != P / (num + 1)) {
div = P / (num + 1) + 1;
num++;
}
}
}
return ans;
}
};
#line 8 "math/verify/verify_math_015_remainder_sum.cpp"
// Verified on Mar 30, 2019
// Educational Codeforces Round 5 E: Sum of Remainders
// Judge: https://codeforces.com/contest/616/problem/E
void ECR005_E() {
long long int N, M; cin >> N >> M;
using mint = ModInt<1000000007>;
RemainderSum<mint> rs(N);
cout << rs.sum_func(M) << endl;
}
// Verified on Mar 30, 2019
// yukicoder No. 752: mod 数列
// Judge: https://yukicoder.me/problems/no/752
void yuki_752() {
long long int P, Q; cin >> P >> Q;
RemainderSum<long long int> rs(P);
while(Q--) {
long long int l, r; cin >> l >> r;
cout << rs.sum_func(l, r) << endl;
}
}
int main() {
ECR005_E();
// yuki_752();
return 0;
}