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#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; }