#include #ifndef ATCODER_MATH_HPP #define ATCODER_MATH_HPP 1 #ifndef ATCODER_INTERNAL_MATH_HPP #define ATCODER_INTERNAL_MATH_HPP 1 #ifdef _MSC_VER #include #endif namespace atcoder { namespace internal { // @param m `1 <= m` // @return x mod m constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } // Fast modular multiplication by barrett reduction // Reference: https://en.wikipedia.org/wiki/Barrett_reduction // NOTE: reconsider after Ice Lake struct barrett { unsigned int _m; unsigned long long im; // @param m `1 <= m < 2^31` explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} // @return m unsigned int umod() const { return _m; } // @param a `0 <= a < m` // @param b `0 <= b < m` // @return `a * b % m` unsigned int mul(unsigned int a, unsigned int b) const { // [1] m = 1 // a = b = im = 0, so okay // [2] m >= 2 // im = ceil(2^64 / m) // -> im * m = 2^64 + r (0 <= r < m) // let z = a*b = c*m + d (0 <= c, d < m) // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2 // ((ab * im) >> 64) == c or c + 1 unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned int v = (unsigned int)(z - x * _m); if (_m <= v) v += _m; return v; } }; // @param n `0 <= n` // @param m `1 <= m` // @return `(x ** n) % m` constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } // Reference: // M. Forisek and J. Jancina, // Fast Primality Testing for Integers That Fit into a Machine Word // @param n `0 <= n` constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template constexpr bool is_prime = is_prime_constexpr(n); // @param b `1 <= b` // @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g constexpr std::pair inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; // Contracts: // [1] s - m0 * a = 0 (mod b) // [2] t - m1 * a = 0 (mod b) // [3] s * |m1| + t * |m0| <= b long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b // [3]: // (s - t * u) * |m1| + t * |m0 - m1 * u| // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u) // = s * |m1| + t * |m0| <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } // by [3]: |m0| <= b/g // by g != b: |m0| < b/g if (m0 < 0) m0 += b / s; return {s, m0}; } // Compile time primitive root // @param m must be prime // @return primitive root (and minimum in now) constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(i)*i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) { x /= i; } } } if (x > 1) { divs[cnt++] = x; } for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } template constexpr int primitive_root = primitive_root_constexpr(m); // @param n `n < 2^32` // @param m `1 <= m < 2^32` // @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64) unsigned long long floor_sum_unsigned(unsigned long long n, unsigned long long m, unsigned long long a, unsigned long long b) { unsigned long long ans = 0; while (true) { if (a >= m) { ans += n * (n - 1) / 2 * (a / m); a %= m; } if (b >= m) { ans += n * (b / m); b %= m; } unsigned long long y_max = a * n + b; if (y_max < m) break; // y_max < m * (n + 1) // floor(y_max / m) <= n n = (unsigned long long)(y_max / m); b = (unsigned long long)(y_max % m); std::swap(m, a); } return ans; } } // namespace internal } // namespace atcoder #endif // ATCODER_INTERNAL_MATH_HPP namespace atcoder { long long pow_mod(long long x, long long n, int m) { assert(0 <= n && 1 <= m); if (m == 1) return 0; internal::barrett bt((unsigned int)(m)); unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m)); while (n) { if (n & 1) r = bt.mul(r, y); y = bt.mul(y, y); n >>= 1; } return r; } long long inv_mod(long long x, long long m) { assert(1 <= m); auto z = internal::inv_gcd(x, m); assert(z.first == 1); return z.second; } // (rem, mod) std::pair crt(const std::vector& r, const std::vector& m) { assert(r.size() == m.size()); int n = int(r.size()); // Contracts: 0 <= r0 < m0 long long r0 = 0, m0 = 1; for (int i = 0; i < n; i++) { assert(1 <= m[i]); long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i]; if (m0 < m1) { std::swap(r0, r1); std::swap(m0, m1); } if (m0 % m1 == 0) { if (r0 % m1 != r1) return {0, 0}; continue; } // assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1) // (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1)); // r2 % m0 = r0 // r2 % m1 = r1 // -> (r0 + x*m0) % m1 = r1 // -> x*u0*g = r1-r0 (mod u1*g) (u0*g = m0, u1*g = m1) // -> x = (r1 - r0) / g * inv(u0) (mod u1) // im = inv(u0) (mod u1) (0 <= im < u1) long long g, im; std::tie(g, im) = internal::inv_gcd(m0, m1); long long u1 = (m1 / g); // |r1 - r0| < (m0 + m1) <= lcm(m0, m1) if ((r1 - r0) % g) return {0, 0}; // u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1) long long x = (r1 - r0) / g % u1 * im % u1; // |r0| + |m0 * x| // < m0 + m0 * (u1 - 1) // = m0 + m0 * m1 / g - m0 // = lcm(m0, m1) r0 += x * m0; m0 *= u1; // -> lcm(m0, m1) if (r0 < 0) r0 += m0; } return {r0, m0}; } long long floor_sum(long long n, long long m, long long a, long long b) { assert(0 <= n && n < (1LL << 32)); assert(1 <= m && m < (1LL << 32)); unsigned long long ans = 0; if (a < 0) { unsigned long long a2 = internal::safe_mod(a, m); ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m); a = a2; } if (b < 0) { unsigned long long b2 = internal::safe_mod(b, m); ans -= 1ULL * n * ((b2 - b) / m); b = b2; } return ans + internal::floor_sum_unsigned(n, m, a, b); } } // namespace atcoder #endif // ATCODER_MATH_HPP #ifndef DEBUG_H_ #define DEBUG_H_ #ifndef CONSTANTS_H_ #define CONSTANTS_H_ // big = 2305843009213693951 = 2^61-1 ~= 2.3*10^18 const int64_t big = std::numeric_limits::max() / 4; #endif // CONSTANTS_H_ #ifndef TYPE_TRAITS_H_ #define TYPE_TRAITS_H_ template struct is_dereferenceable : std::false_type {}; template struct is_dereferenceable())>> : std::true_type {}; template struct is_iterable : std::false_type {}; template struct is_iterable())), decltype(std::end(std::declval()))>> : std::true_type {}; template struct is_applicable : std::false_type {}; template struct is_applicable::value)>> : std::true_type {}; #endif // TYPE_TRAITS_H template void debug(std::ostream& os, const T& value, const Ts&... args); template void debug(std::ostream& os, const T& v) { if constexpr (std::is_same>::value) { if (v == big) { os << "big"; } else { os << v; } } else if constexpr (std::is_same>::value || std::is_same::value) { os << v; } else if constexpr (is_dereferenceable::value) { os << "{"; if (v) { debug(os, *v); } else { os << "nil"; } os << "}"; } else if constexpr (is_iterable::value) { os << "{"; for (auto it = std::begin(v); it != std::end(v); ++it) { if (it != std::begin(v)) os << ", "; debug(os, *it); } os << "}"; } else if constexpr (is_applicable::value) { os << "{"; std::apply([&os](const auto&... args) { debug(os, args...); }, v); os << "}"; } else { os << v; } } template void debug(std::ostream& os, const T& value, const Ts&... args) { debug(os, value); os << ", "; debug(os, args...); } #if DEBUG #define dbg(...) \ do { \ cerr << #__VA_ARGS__ << ": "; \ debug(std::cerr, __VA_ARGS__); \ cerr << " (L" << __LINE__ << ")\n"; \ } while (0) #else #define dbg(...) #endif #endif // DEBUG_H_ #ifndef FIX_H_ #define FIX_H_ template struct FixPoint { F f; template decltype(auto) operator()(Args&&... args) const { return f(std::ref(*this), std::forward(args)...); } }; template FixPoint> Fix(F&& f) { return {std::forward(f)}; } #endif // FIX_H_ #ifndef IO_H_ #define IO_H void read_from_cin() {} template void read_from_cin(T& value, Ts&... args) { std::cin >> value; read_from_cin(args...); } #define rd(type, ...) \ type __VA_ARGS__; \ read_from_cin(__VA_ARGS__); #define ints(...) rd(int, __VA_ARGS__); #define strings(...) rd(string, __VA_ARGS__); const char *yes_str = "Yes", *no_str = "No"; template void write_to_cout(const T& value) { if constexpr (std::is_same::value) { std::cout << (value ? yes_str : no_str); } else if constexpr (is_iterable::value && !std::is_same::value) { for (auto it = std::begin(value); it != std::end(value); ++it) { if (it != std::begin(value)) std::cout << " "; std::cout << *it; } } else { std::cout << value; } } template void write_to_cout(const T& value, const Ts&... args) { write_to_cout(value); std::cout << ' '; write_to_cout(args...); } #define wt(...) \ do { \ write_to_cout(__VA_ARGS__); \ cout << '\n'; \ } while (0) template std::istream& operator>>(std::istream& is, std::vector& v) { for (T& vi : v) is >> vi; return is; } template std::istream& operator>>(std::istream& is, std::pair& p) { is >> p.first >> p.second; return is; } #endif // IO_H_ #ifndef MACROS_H_ #define MACROS_H_ #define all(x) (x).begin(), (x).end() #define eb(...) emplace_back(__VA_ARGS__) #define pb(...) push_back(__VA_ARGS__) #define dispatch(_1, _2, _3, name, ...) name #define as_i64(x) \ ( \ [] { \ static_assert( \ std::is_integral< \ typename std::remove_reference::type>::value, \ "rep macro supports std integral types only"); \ }, \ static_cast(x)) #define rep3(i, a, b) for (int64_t i = as_i64(a); i < as_i64(b); ++i) #define rep2(i, n) rep3(i, 0, n) #define rep1(n) rep2(_loop_variable_, n) #define rep(...) dispatch(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__) #define rrep3(i, a, b) for (int64_t i = as_i64(b) - 1; i >= as_i64(a); --i) #define rrep2(i, n) rrep3(i, 0, n) #define rrep1(n) rrep2(_loop_variable_, n) #define rrep(...) dispatch(__VA_ARGS__, rrep3, rrep2, rrep1)(__VA_ARGS__) #define each3(k, v, c) for (auto&& [k, v] : c) #define each2(e, c) for (auto&& e : c) #define each(...) dispatch(__VA_ARGS__, each3, each2)(__VA_ARGS__) template bool chmax(T& a, U b) { if (a < b) { a = b; return true; } return false; } template bool chmin(T& a, U b) { if (a > b) { a = b; return true; } return false; } template auto max(T a, U b) { return a > b ? a : b; } template auto min(T a, U b) { return a < b ? a : b; } template auto max(const T& v) { return *std::max_element(v.begin(), v.end()); } template auto min(const T& v) { return *std::min_element(v.begin(), v.end()); } template int64_t sz(const T& v) { return std::size(v); } template int64_t popcount(T i) { return std::bitset::digits>(i).count(); } template bool hasbit(T s, int i) { return std::bitset::digits>(s)[i]; } template auto div_floor(T n, U d) { if (d < 0) { n = -n; d = -d; } if (n < 0) { return -((-n + d - 1) / d); } return n / d; }; template auto div_ceil(T n, U d) { if (d < 0) { n = -n; d = -d; } if (n < 0) { return -(-n / d); } return (n + d - 1) / d; } template bool even(T x) { return x % 2 == 0; } std::array, 4> adjacent(int64_t i, int64_t j) { return {{{i + 1, j}, {i, j + 1}, {i - 1, j}, {i, j - 1}}}; } bool inside(int64_t i, int64_t j, int64_t I, int64_t J) { return 0 <= i && i < I && 0 <= j && j < J; } template void sort(T& v) { return std::sort(v.begin(), v.end()); } template void sort(T& v, Compare comp) { return std::sort(v.begin(), v.end(), comp); } template void reverse(T& v) { return std::reverse(v.begin(), v.end()); } template typename T::value_type accumulate(const T& v) { return std::accumulate(v.begin(), v.end(), typename T::value_type()); } using i64 = int64_t; using i32 = int32_t; template using low_priority_queue = std::priority_queue, std::greater>; template using V = std::vector; template using VV = V>; #endif // MACROS_H_ void Main(); int main() { std::ios_base::sync_with_stdio(false); std::cin.tie(NULL); std::cout << std::fixed << std::setprecision(20); Main(); return 0; } using namespace std; #define int i64 void Main() { ints(n, m); V a(n), b(m); cin >> a >> b; int ans = 0; rep(i, n) rep(j, m) { ans += atcoder::floor_sum(b[j] + 1, b[j], a[i], 0) * 2; ans %= int(1e9 + 7); } wt(ans); }