// need
#include <iostream>
#include <algorithm>

// data structure
#include <bitset>
//#include <list>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#include <array>
//#include <tuple>
//#include <unordered_map>
#include <unordered_set>
#include <complex>
//#include <deque>
#include<valarray>

// stream
//#include <istream>
//#include <sstream>
//#include <ostream>
//#include <fstream>

// etc
#include <cmath>
#include <cassert>
#include <functional>
#include <iomanip>
//#include <typeinfo>
#include <chrono>
#include <random>
#include <numeric>

// input
#define INIT std::ios::sync_with_stdio(false);std::cin.tie(0);
#define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__);
template<typename T> void MACRO_VAR_Scan(T& t) { std::cin >> t; }
template<typename First, typename...Rest>void MACRO_VAR_Scan(First& first, Rest&...rest) { std::cin >> first; MACRO_VAR_Scan(rest...); }
#define VEC_ROW(type, n, ...)std::vector<type> __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int i=0; i<n; ++i){MACRO_VEC_ROW_Scan(i, __VA_ARGS__);}
template<typename T> void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Init(int n, First& first, Rest&...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); }
template<typename T> void MACRO_VEC_ROW_Scan(int p, T& t) { std::cin >> t[p]; }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Scan(int p, First& first, Rest&...rest) { std::cin >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); }
#define VEC(type, c, n) std::vector<type> c(n);for(auto& i:c)std::cin>>i;
#define MAT(type, c, m, n) std::vector<std::vector<type>> c(m, std::vector<type>(n));for(auto& r:c)for(auto& i:r)std::cin>>i;

// output
#define OUT(d) std::cout<<d;
#define FOUT(n, d) std::cout<<std::fixed<<std::setprecision(n)<<d;
#define SOUT(n, c, d) std::cout<<std::setw(n)<<std::setfill(c)<<d;
#define SP std::cout<<" ";
#define TAB std::cout<<"\t";
#define BR std::cout<<"\n";
#define SPBR(i, n) std::cout<<(i + 1 == n ? '\n' : ' ');
#define ENDL std::cout<<std::endl;
#define FLUSH std::cout<<std::flush;
#define SHOW(d) {std::cerr << #d << "\t:" << d << "\n";}
#define SHOWVECTOR(v) {std::cerr << #v << "\t:";for(const auto& xxx : v){std::cerr << xxx << " ";}std::cerr << "\n";}
#define SHOWVECTOR2(v) {std::cerr << #v << "\t:\n";for(const auto& xxx : v){for(const auto& yyy : xxx){std::cerr << yyy << " ";}std::cerr << "\n";}}
#define SHOWQUEUE(a) {auto tmp(a);std::cerr << #a << "\t:";while(!tmp.empty()){std::cerr << tmp.front() << " ";tmp.pop();}std::cerr << "\n";}

// utility
#define ALL(a) (a).begin(),(a).end()
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define RFOR(i, a, b) for(int i=(b)-1;i>=(a);--i)
#define REP(i, n) for(int i=0;i<int(n);++i)
#define RREP(i, n) for(int i=int(n)-1;i>=0;--i)
#define FORLL(i, a, b) for(ll i=ll(a);i<ll(b);++i)
#define RFORLL(i, a, b) for(ll i=ll(b)-1;i>=ll(a);--i)
#define REPLL(i, n) for(ll i=0;i<ll(n);++i)
#define RREPLL(i, n) for(ll i=ll(n)-1;i>=0;--i)
#define IN(a, x, b) (a<=x && x<b)
template<typename T> inline T CHMAX(T& a, const T b) { return a = (a < b) ? b : a; }
template<typename T> inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; }
#define EXCEPTION(msg) throw std::string("Exception : " msg " [ in ") + __func__ + " : " + std::to_string(__LINE__) + " lines ]"
#define TRY(cond, msg) try {if (cond) EXCEPTION(msg);}catch (std::string s) {std::cerr << s << std::endl;}
void CHECKTIME(std::function<void()> f) { auto start = std::chrono::system_clock::now(); f(); auto end = std::chrono::system_clock::now(); auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start)).count(); std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\n"; }

// test
template<class T> std::vector<std::vector<T>> VV(int n) {
	return std::vector<std::vector<T>>(n);
}
template<class T> std::vector<std::vector<T>> VV(int n, int m, T init = T()) {
	return std::vector<std::vector<T>>(n, std::vector<T>(m, init));
}
template<typename S, typename T>
std::ostream& operator<<(std::ostream& os, std::pair<S, T> p) {
	os << "(" << p.first << ", " << p.second << ")"; return os;
}

// type/const

#define int ll
using ll = long long;
using ull = unsigned long long;
using PAIR = std::pair<int, int>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = 1 << 30;                          // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;              // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                          // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62);  // 9.22x10^18
constexpr double EPS = 1e-7;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;

class ModInt {
	friend std::istream& operator>>(std::istream& is, ModInt& obj);
private:
	int M;
	bool M_is_prime;
	bool isPrime() {
		for (int i = 2; i * i <= M; ++i) if (M%i == 0) return false;
		return true;
	}
public:
	int val;
	ModInt() : val(0), M(MOD), M_is_prime(true) {}
	ModInt(int n) : val(n%MOD), M(MOD), M_is_prime(true) {}
	ModInt(int n, int m) : val(n%m), M(m), M_is_prime(isPrime()) {}
	ModInt& operator=(const signed& r) {
		val = r % M;
		return *this;
	}
	ModInt operator+() const { return *this; }
	ModInt operator-() const { return ModInt(M - val); }
	ModInt& operator+=(const ModInt& r) {
		val += r.val;
		val %= M;
		return *this;
	}
	ModInt& operator+=(const int& r) {
		*this += ModInt(r);
		return *this;
	}
	ModInt& operator-=(const ModInt& r) { return *this += -r; }
	ModInt& operator-=(const int& r) { return *this += -r + M; }
	ModInt& operator++() { return *this += 1; }
	ModInt& operator++(signed tmp) { return *this += 1; }
	ModInt& operator--() { return *this -= 1; }
	ModInt& operator--(signed tmp) { return *this -= 1; }
	ModInt& operator*=(const ModInt& r) {
		val *= r.val;
		val %= M;
		return *this;
	}
	ModInt& operator*=(const int& r) {
		val *= r%M;
		val %= M;
		return *this;
	}
	ModInt& operator^=(int p) { // O(log(p))
		ModInt res(1);
		while (p) {
			if (p & 1) res *= *this;
			*this *= *this;
			p >>= 1;
		}
		return *this = res;
	}
	ModInt& operator^=(const ModInt& r) { // O(log(p))
		int p = r.val;
		return *this ^= p;
	}
	ModInt& operator/=(ModInt r) { // M must be a prime.
		assert(M_is_prime);
		return *this *= r ^= (M - 2);
	}
	ModInt& operator/=(int r) { // M must be a prime.
		return *this /= ModInt(r);
	}
	ModInt operator+(const ModInt& r) const {
		auto res(*this);
		return res += r;
	}
	ModInt operator-(const ModInt& r) const {
		auto res(*this);
		return res -= r;
	}
	ModInt operator*(const ModInt& r) const {
		auto res(*this);
		return res *= r;
	}
	ModInt operator^(const ModInt& r) const {
		auto res(*this);
		return res ^= r;
	}
	ModInt operator/(const ModInt& r) const { // M must be a prime.
		auto res(*this);
		return res /= r;
	}
	ModInt operator+(const int& r) const {
		auto res(*this);
		return res += r;
	}
	ModInt operator-(const int& r) const {
		auto res(*this);
		return res -= r;
	}
	ModInt operator*(const int& r) const {
		auto res(*this);
		return res *= r;
	}
	ModInt operator^(const int& r) const {
		auto res(*this);
		return res ^= r;
	}
	ModInt operator/(const int& r) const { // M must be a prime.
		auto res(*this);
		return res /= r;
	}
};
std::ostream& operator<<(std::ostream& os, const ModInt& obj) {
	os << obj.val;
	return os;
}
/* friend */ std::istream& operator>>(std::istream& is, ModInt& obj) {
	is >> obj.val;
	obj.val %= obj.M;
	return is;
}
/** ModInt **/

signed main() {
	INIT;
	VAR(int, _n, _m);
	ModInt ans, n(_n), m(_m);
	if (_n == 1) {
		OUT(++_m % MOD)BR;
		return 0;
	}
	ModInt t(_m / (_n - 1));
	ans += m + 1;
	ans += (m + 1) * 2 * t - (n - 1) * t * (t + 1);
	OUT(ans)BR;
	return 0;
}
### Prompt

Please create a solution in CPP to the following problem:

B: Ebi-chan and Integer Sequences-

problem

Ebi-chan likes sequences. I especially like arithmetic progressions. This time, I decided to create a sequence that meets the following conditions.

* Arithmetic progression of length n
* When the i-th element of the sequence is defined as s_i, all s_i (1 \ leq i \ leq n) are integers that satisfy 0 \ leq s_i \ leq m.



How many sequences are there that satisfy the above conditions? However, the answer can be very large, so print the remainder after dividing by 10 ^ 9 + 7.

Input format

Input is given in one line.


n m

n represents the length of the sequence.

Constraint

* 1 \ leq n \ leq 10 ^ {15}
* 0 \ leq m \ leq 10 ^ {15}



Output format

Divide the number of arithmetic progressions that satisfy the condition by 10 ^ 9 + 7 and output the remainder in one row.

Input example 1


3 9

Output example 1


50

Input example 2


10000000000 10000000000

Output example 2


999999942

Note that the input does not fit in a 32-bit integer.





Example

Input

3 9


Output

50

### Response

```cpp
// need
#include <iostream>
#include <algorithm>

// data structure
#include <bitset>
//#include <list>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#include <array>
//#include <tuple>
//#include <unordered_map>
#include <unordered_set>
#include <complex>
//#include <deque>
#include<valarray>

// stream
//#include <istream>
//#include <sstream>
//#include <ostream>
//#include <fstream>

// etc
#include <cmath>
#include <cassert>
#include <functional>
#include <iomanip>
//#include <typeinfo>
#include <chrono>
#include <random>
#include <numeric>

// input
#define INIT std::ios::sync_with_stdio(false);std::cin.tie(0);
#define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__);
template<typename T> void MACRO_VAR_Scan(T& t) { std::cin >> t; }
template<typename First, typename...Rest>void MACRO_VAR_Scan(First& first, Rest&...rest) { std::cin >> first; MACRO_VAR_Scan(rest...); }
#define VEC_ROW(type, n, ...)std::vector<type> __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int i=0; i<n; ++i){MACRO_VEC_ROW_Scan(i, __VA_ARGS__);}
template<typename T> void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Init(int n, First& first, Rest&...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); }
template<typename T> void MACRO_VEC_ROW_Scan(int p, T& t) { std::cin >> t[p]; }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Scan(int p, First& first, Rest&...rest) { std::cin >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); }
#define VEC(type, c, n) std::vector<type> c(n);for(auto& i:c)std::cin>>i;
#define MAT(type, c, m, n) std::vector<std::vector<type>> c(m, std::vector<type>(n));for(auto& r:c)for(auto& i:r)std::cin>>i;

// output
#define OUT(d) std::cout<<d;
#define FOUT(n, d) std::cout<<std::fixed<<std::setprecision(n)<<d;
#define SOUT(n, c, d) std::cout<<std::setw(n)<<std::setfill(c)<<d;
#define SP std::cout<<" ";
#define TAB std::cout<<"\t";
#define BR std::cout<<"\n";
#define SPBR(i, n) std::cout<<(i + 1 == n ? '\n' : ' ');
#define ENDL std::cout<<std::endl;
#define FLUSH std::cout<<std::flush;
#define SHOW(d) {std::cerr << #d << "\t:" << d << "\n";}
#define SHOWVECTOR(v) {std::cerr << #v << "\t:";for(const auto& xxx : v){std::cerr << xxx << " ";}std::cerr << "\n";}
#define SHOWVECTOR2(v) {std::cerr << #v << "\t:\n";for(const auto& xxx : v){for(const auto& yyy : xxx){std::cerr << yyy << " ";}std::cerr << "\n";}}
#define SHOWQUEUE(a) {auto tmp(a);std::cerr << #a << "\t:";while(!tmp.empty()){std::cerr << tmp.front() << " ";tmp.pop();}std::cerr << "\n";}

// utility
#define ALL(a) (a).begin(),(a).end()
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define RFOR(i, a, b) for(int i=(b)-1;i>=(a);--i)
#define REP(i, n) for(int i=0;i<int(n);++i)
#define RREP(i, n) for(int i=int(n)-1;i>=0;--i)
#define FORLL(i, a, b) for(ll i=ll(a);i<ll(b);++i)
#define RFORLL(i, a, b) for(ll i=ll(b)-1;i>=ll(a);--i)
#define REPLL(i, n) for(ll i=0;i<ll(n);++i)
#define RREPLL(i, n) for(ll i=ll(n)-1;i>=0;--i)
#define IN(a, x, b) (a<=x && x<b)
template<typename T> inline T CHMAX(T& a, const T b) { return a = (a < b) ? b : a; }
template<typename T> inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; }
#define EXCEPTION(msg) throw std::string("Exception : " msg " [ in ") + __func__ + " : " + std::to_string(__LINE__) + " lines ]"
#define TRY(cond, msg) try {if (cond) EXCEPTION(msg);}catch (std::string s) {std::cerr << s << std::endl;}
void CHECKTIME(std::function<void()> f) { auto start = std::chrono::system_clock::now(); f(); auto end = std::chrono::system_clock::now(); auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start)).count(); std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\n"; }

// test
template<class T> std::vector<std::vector<T>> VV(int n) {
	return std::vector<std::vector<T>>(n);
}
template<class T> std::vector<std::vector<T>> VV(int n, int m, T init = T()) {
	return std::vector<std::vector<T>>(n, std::vector<T>(m, init));
}
template<typename S, typename T>
std::ostream& operator<<(std::ostream& os, std::pair<S, T> p) {
	os << "(" << p.first << ", " << p.second << ")"; return os;
}

// type/const

#define int ll
using ll = long long;
using ull = unsigned long long;
using PAIR = std::pair<int, int>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = 1 << 30;                          // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;              // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                          // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62);  // 9.22x10^18
constexpr double EPS = 1e-7;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;

class ModInt {
	friend std::istream& operator>>(std::istream& is, ModInt& obj);
private:
	int M;
	bool M_is_prime;
	bool isPrime() {
		for (int i = 2; i * i <= M; ++i) if (M%i == 0) return false;
		return true;
	}
public:
	int val;
	ModInt() : val(0), M(MOD), M_is_prime(true) {}
	ModInt(int n) : val(n%MOD), M(MOD), M_is_prime(true) {}
	ModInt(int n, int m) : val(n%m), M(m), M_is_prime(isPrime()) {}
	ModInt& operator=(const signed& r) {
		val = r % M;
		return *this;
	}
	ModInt operator+() const { return *this; }
	ModInt operator-() const { return ModInt(M - val); }
	ModInt& operator+=(const ModInt& r) {
		val += r.val;
		val %= M;
		return *this;
	}
	ModInt& operator+=(const int& r) {
		*this += ModInt(r);
		return *this;
	}
	ModInt& operator-=(const ModInt& r) { return *this += -r; }
	ModInt& operator-=(const int& r) { return *this += -r + M; }
	ModInt& operator++() { return *this += 1; }
	ModInt& operator++(signed tmp) { return *this += 1; }
	ModInt& operator--() { return *this -= 1; }
	ModInt& operator--(signed tmp) { return *this -= 1; }
	ModInt& operator*=(const ModInt& r) {
		val *= r.val;
		val %= M;
		return *this;
	}
	ModInt& operator*=(const int& r) {
		val *= r%M;
		val %= M;
		return *this;
	}
	ModInt& operator^=(int p) { // O(log(p))
		ModInt res(1);
		while (p) {
			if (p & 1) res *= *this;
			*this *= *this;
			p >>= 1;
		}
		return *this = res;
	}
	ModInt& operator^=(const ModInt& r) { // O(log(p))
		int p = r.val;
		return *this ^= p;
	}
	ModInt& operator/=(ModInt r) { // M must be a prime.
		assert(M_is_prime);
		return *this *= r ^= (M - 2);
	}
	ModInt& operator/=(int r) { // M must be a prime.
		return *this /= ModInt(r);
	}
	ModInt operator+(const ModInt& r) const {
		auto res(*this);
		return res += r;
	}
	ModInt operator-(const ModInt& r) const {
		auto res(*this);
		return res -= r;
	}
	ModInt operator*(const ModInt& r) const {
		auto res(*this);
		return res *= r;
	}
	ModInt operator^(const ModInt& r) const {
		auto res(*this);
		return res ^= r;
	}
	ModInt operator/(const ModInt& r) const { // M must be a prime.
		auto res(*this);
		return res /= r;
	}
	ModInt operator+(const int& r) const {
		auto res(*this);
		return res += r;
	}
	ModInt operator-(const int& r) const {
		auto res(*this);
		return res -= r;
	}
	ModInt operator*(const int& r) const {
		auto res(*this);
		return res *= r;
	}
	ModInt operator^(const int& r) const {
		auto res(*this);
		return res ^= r;
	}
	ModInt operator/(const int& r) const { // M must be a prime.
		auto res(*this);
		return res /= r;
	}
};
std::ostream& operator<<(std::ostream& os, const ModInt& obj) {
	os << obj.val;
	return os;
}
/* friend */ std::istream& operator>>(std::istream& is, ModInt& obj) {
	is >> obj.val;
	obj.val %= obj.M;
	return is;
}
/** ModInt **/

signed main() {
	INIT;
	VAR(int, _n, _m);
	ModInt ans, n(_n), m(_m);
	if (_n == 1) {
		OUT(++_m % MOD)BR;
		return 0;
	}
	ModInt t(_m / (_n - 1));
	ans += m + 1;
	ans += (m + 1) * 2 * t - (n - 1) * t * (t + 1);
	OUT(ans)BR;
	return 0;
}
```