#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

// #pragma comment(linker, "/stack:200000000")

#include <bits/stdc++.h>

#include <limits>
#include <type_traits>

namespace suisen {
// ! utility
template <typename ...Types>
using constraints_t = std::enable_if_t<std::conjunction_v<Types...>, std::nullptr_t>;
template <bool cond_v, typename Then, typename OrElse>
constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) {
    if constexpr (cond_v) {
        return std::forward<Then>(then);
    } else {
        return std::forward<OrElse>(or_else);
    }
}

// ! function
template <typename ReturnType, typename Callable, typename ...Args>
using is_same_as_invoke_result = std::is_same<std::invoke_result_t<Callable, Args...>, ReturnType>;
template <typename F, typename T>
using is_uni_op = is_same_as_invoke_result<T, F, T>;
template <typename F, typename T>
using is_bin_op = is_same_as_invoke_result<T, F, T, T>;

template <typename Comparator, typename T>
using is_comparator = std::is_same<std::invoke_result_t<Comparator, T, T>, bool>;

// ! integral
template <typename T, typename = constraints_t<std::is_integral<T>>>
constexpr int bit_num = std::numeric_limits<std::make_unsigned_t<T>>::digits;
template <typename T, unsigned int n>
struct is_nbit { static constexpr bool value = bit_num<T> == n; };
template <typename T, unsigned int n>
static constexpr bool is_nbit_v = is_nbit<T, n>::value;

// ?
template <typename T>
struct safely_multipliable {};
template <>
struct safely_multipliable<int> { using type = long long; };
template <>
struct safely_multipliable<long long> { using type = __int128_t; };
template <>
struct safely_multipliable<unsigned int> { using type = unsigned long long; };
template <>
struct safely_multipliable<unsigned long long> { using type = __uint128_t; };
template <>
struct safely_multipliable<float> { using type = float; };
template <>
struct safely_multipliable<double> { using type = double; };
template <>
struct safely_multipliable<long double> { using type = long double; };
template <typename T>
using safely_multipliable_t = typename safely_multipliable<T>::type;

} // namespace suisen

// ! type aliases
using i128 = __int128_t;
using u128 = __uint128_t;
using ll = long long;
using uint = unsigned int;
using ull  = unsigned long long;

template <typename T> using vec  = std::vector<T>;
template <typename T> using vec2 = vec<vec <T>>;
template <typename T> using vec3 = vec<vec2<T>>;
template <typename T> using vec4 = vec<vec3<T>>;

template <typename T>
using pq_greater = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <typename T, typename U>
using umap = std::unordered_map<T, U>;

// ! macros (capital: internal macro)
#define OVERLOAD2(_1,_2,name,...) name
#define OVERLOAD3(_1,_2,_3,name,...) name
#define OVERLOAD4(_1,_2,_3,_4,name,...) name

#define REP4(i,l,r,s)  for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l);i<(r);i+=(s))
#define REP3(i,l,r)    REP4(i,l,r,1)
#define REP2(i,n)      REP3(i,0,n)
#define REPINF3(i,l,s) for(std::remove_reference_t<std::remove_const_t<decltype(l)>>i=(l);;i+=(s))
#define REPINF2(i,l)   REPINF3(i,l,1)
#define REPINF1(i)     REPINF2(i,0)
#define RREP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l)+fld((r)-(l)-1,s)*(s);i>=(l);i-=(s))
#define RREP3(i,l,r)   RREP4(i,l,r,1)
#define RREP2(i,n)     RREP3(i,0,n)

#define rep(...)    OVERLOAD4(__VA_ARGS__, REP4   , REP3   , REP2   )(__VA_ARGS__)
#define rrep(...)   OVERLOAD4(__VA_ARGS__, RREP4  , RREP3  , RREP2  )(__VA_ARGS__)
#define repinf(...) OVERLOAD3(__VA_ARGS__, REPINF3, REPINF2, REPINF1)(__VA_ARGS__)

#define CAT_I(a, b) a##b
#define CAT(a, b) CAT_I(a, b)
#define UNIQVAR(tag) CAT(tag, __LINE__)
#define loop(n) for (std::remove_reference_t<std::remove_const_t<decltype(n)>> UNIQVAR(loop_variable) = n; UNIQVAR(loop_variable) --> 0;)

#define all(iterable) (iterable).begin(), (iterable).end()
#define input(type, ...) type __VA_ARGS__; read(__VA_ARGS__)

// ! I/O utilities

// pair
template <typename T, typename U>
std::ostream& operator<<(std::ostream& out, const std::pair<T, U> &a) {
    return out << a.first << ' ' << a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::ostream& operator<<(std::ostream& out, const std::tuple<Args...> &a) {
    if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) {
        return out;
    } else {
        out << std::get<N>(a);
        if constexpr (N + 1 < std::tuple_size_v<std::tuple<Args...>>) {
            out << ' ';
        }
        return operator<<<N + 1>(out, a);
    }
}
// vector
template <typename T>
std::ostream& operator<<(std::ostream& out, const std::vector<T> &a) {
    for (auto it = a.begin(); it != a.end();) {
        out << *it;
        if (++it != a.end()) out << ' ';
    }
    return out;
}
// array
template <typename T, size_t N>
std::ostream& operator<<(std::ostream& out, const std::array<T, N> &a) {
    for (auto it = a.begin(); it != a.end();) {
        out << *it;
        if (++it != a.end()) out << ' ';
    }
    return out;
}
inline void print() { std::cout << '\n'; }
template <typename Head, typename... Tail>
inline void print(const Head &head, const Tail &...tails) {
    std::cout << head;
    if (sizeof...(tails)) std::cout << ' ';
    print(tails...);
}
template <typename Iterable>
auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) {
    for (auto it = v.begin(); it != v.end();) {
        std::cout << *it;
        if (++it != v.end()) std::cout << sep;
    }
    std::cout << end;
}

// pair
template <typename T, typename U>
std::istream& operator>>(std::istream& in, std::pair<T, U> &a) {
    return in >> a.first >> a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::istream& operator>>(std::istream& in, std::tuple<Args...> &a) {
    if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) {
        return in;
    } else {
        return operator>><N + 1>(in >> std::get<N>(a), a);
    }
}
// vector
template <typename T>
std::istream& operator>>(std::istream& in, std::vector<T> &a) {
    for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
    return in;
}
// array
template <typename T, size_t N>
std::istream& operator>>(std::istream& in, std::array<T, N> &a) {
    for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
    return in;
}
template <typename ...Args>
void read(Args &...args) {
    ( std::cin >> ... >> args );
}

// ! integral utilities

// Returns pow(-1, n)
template <typename T>
constexpr inline int pow_m1(T n) {
    return -(n & 1) | 1;
}
// Returns pow(-1, n)
template <>
constexpr inline int pow_m1<bool>(bool n) {
    return -int(n) | 1;
}

// Returns floor(x / y)
template <typename T>
constexpr inline T fld(const T x, const T y) {
    return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y;
}
template <typename T>
constexpr inline T cld(const T x, const T y) {
    return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y;
}

template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int popcount(const T x) { return __builtin_popcount(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int popcount(const T x) { return __builtin_popcount(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int popcount(const T x) { return __builtin_popcountll(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x)   : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x)   : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x)   : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x)   : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num<T>; }
template <typename T>
constexpr inline int floor_log2(const T x) { return suisen::bit_num<T> - 1 - count_lz(x); }
template <typename T>
constexpr inline int ceil_log2(const T x)  { return floor_log2(x) + ((x & -x) != x); }
template <typename T>
constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; }
template <typename T>
constexpr inline int parity(const T x) { return popcount(x) & 1; }

struct all_subset {
    struct all_subset_iter {
        const int s; int t;
        constexpr all_subset_iter(int s) : s(s), t(s + 1) {}
        constexpr auto operator*() const { return t; }
        constexpr auto operator++() {}
        constexpr auto operator!=(std::nullptr_t) { return t ? (--t &= s, true) : false; }
    };
    int s;
    constexpr all_subset(int s) : s(s) {}
    constexpr auto begin() { return all_subset_iter(s); }
    constexpr auto end()   { return nullptr; }
};

// ! container

template <typename T, typename Comparator, suisen::constraints_t<suisen::is_comparator<Comparator, T>> = nullptr>
auto priqueue_comp(const Comparator comparator) {
    return std::priority_queue<T, std::vector<T>, Comparator>(comparator);
}

template <typename Iterable>
auto isize(const Iterable &iterable) -> decltype(int(iterable.size())) {
    return iterable.size();
}

template <typename T, typename Gen, suisen::constraints_t<suisen::is_same_as_invoke_result<T, Gen, int>> = nullptr>
auto generate_vector(int n, Gen generator) {
    std::vector<T> v(n);
    for (int i = 0; i < n; ++i) v[i] = generator(i);
    return v;
}
template <typename T>
auto generate_range_vector(T l, T r) {
    return generate_vector(r - l, [l](int i) { return l + i; });
}
template <typename T>
auto generate_range_vector(T n) {
    return generate_range_vector(0, n);
}

template <typename T>
void sort_unique_erase(std::vector<T> &a) {
    std::sort(a.begin(), a.end());
    a.erase(std::unique(a.begin(), a.end()), a.end());
}

template <typename InputIterator, typename BiConsumer>
auto foreach_adjacent_values(InputIterator first, InputIterator last, BiConsumer f) -> decltype(f(*first++, *last), void()) {
    if (first != last) for (auto itr = first, itl = itr++; itr != last; itl = itr++) f(*itl, *itr);
}
template <typename Container, typename BiConsumer>
auto foreach_adjacent_values(Container c, BiConsumer f) -> decltype(c.begin(), c.end(), void()){
    foreach_adjacent_values(c.begin(), c.end(), f);
}

// ! other utilities

// x <- min(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmin(T &x, const T &y) {
    if (y >= x) return false;
    x = y;
    return true;
}
// x <- max(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmax(T &x, const T &y) {
    if (y <= x) return false;
    x = y;
    return true;
}

namespace suisen {}
using namespace suisen;
using namespace std;

struct io_setup {
    io_setup(int precision = 20) {
        std::ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
        std::cout << std::fixed << std::setprecision(precision);
    }
} io_setup_{};

// ! code from here

#include <cassert>
#include <numeric>

#ifdef _MSC_VER
#include <intrin.h>
#endif

#include <utility>

#ifdef _MSC_VER
#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 <int n> 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<long long, long long> 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 <int m> 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

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal

}  // namespace atcoder

using mint = atcoder::modint1000000007;

std::istream& operator>>(std::istream& in, mint& a) {
    long long e; in >> e; a = e;
    return in;
}

std::ostream& operator<<(std::ostream& out, const mint& a) {
    out << a.val();
    return out;
}

#include <algorithm>
#include <vector>

namespace suisen {
    struct Permutation : public std::vector<int> {
        using base_type = std::vector<int>;
        using base_type::base_type;

        Permutation() : Permutation(0) {}
        Permutation(std::size_t n) : Permutation(int(n)) {}
        Permutation(int n) : base_type(n) {
            std::iota(begin(), end(), 0);
        }
        Permutation(const std::vector<int>& a) : std::vector<int>(a) {}
        Permutation(std::vector<int>&& a) : std::vector<int>(std::move(a)) {}

        // returns b s.t. b[i] = a[p[i]]
        template <typename T>
        std::vector<T> permute(const std::vector<T>& a) const {
            const int n = a.size();
            std::vector<T> res(n);
            for (int i = 0; i < n; ++i) res[i] = a[(*this)[i]];
            return res;
        }
        // returns b s.t. b[p[i]] = a[i]
        template <typename T>
        std::vector<T> inv_permute(const std::vector<T>& a) const {
            const int n = a.size();
            std::vector<T> res(n);
            for (int i = 0; i < n; ++i) res[(*this)[i]] = a[i];
            return res;
        }

        // returns p * q s.t. (p * q)[i] = p[q[i]]
        friend Permutation operator*(const Permutation& p, const Permutation& q) {
            return q.permute(p);
        }
        Permutation& operator*=(const Permutation& q) {
            return *this = *this * q;
        }
        Permutation inv() const {
            const int n = size();
            Permutation res(n);
            for (int i = 0; i < n; ++i) res[(*this)[i]] = i;
            return res;
        }
        Permutation pow(long long k) const {
            assert(k >= 0);
            const int n = size();
            std::vector<int8_t> seen(n, false);
            Permutation res(n);
            for (int s = 0; s < n; ++s) {
                if (seen[s]) continue;
                std::vector<int> cycle { s };
                for (int v = (*this)[s]; v != s; v = (*this)[v]) cycle.push_back(v);
                const int l = cycle.size();
                for (int j = 0; j < l; ++j) {
                    int v = cycle[j];
                    seen[v] = true;
                    res[v] = cycle[(j + k) % l];
                }
            }
            return res;
        }

        template <typename T, typename Comp = std::less<T>>
        static Permutation index_sort(const std::vector<T>& a, Comp comp = Comp{}) {
            Permutation p(a.size());
            std::sort(p.begin(), p.end(), [&](int i, int j) { return comp(a[i], a[j]); });
            return p;
        }
    };

    template <typename hash_t>
    struct PermutationHash {
        hash_t operator()(const Permutation &p) const {
            return hash(p);
        }
        /**
         * minimal perfect hash function for permutations.
         * complexity: O(n) time, O(n) extra space
         * reference: https://twitter.com/noshi91/status/1452081886025555972?s=20
         */
        static hash_t hash(const Permutation &per) {
            hash_t h = 0;
            const int n = per.size();
            Permutation p = per;
            Permutation q = per.inv();
            for (int i = n - 1; i >= 0; --i) {
                h = h * (i + 1) + p[i];
                p[q[i]] = p[i];
                q[p[i]] = q[i];
            }
            return h;
        }
        static Permutation unhash(int n, hash_t h) {
            Permutation p = Permutation(n), q = p;
            for (int i = 0; i < n; ++i) {
                p[i] = h % (i + 1), q[i] = q[p[i]];
                q[p[i]] = p[q[i]] = i;
                h /= i + 1;
            }
            return p;
        }
    };
} // namespace suisen

namespace suisen {
template <typename T, typename U>
std::pair<T, U>& operator+=(std::pair<T, U> &p1, const std::pair<T, U> &p2) {
    p1.first += p2.first, p1.second += p2.second;
    return p1;
}
template <typename T, typename U>
std::pair<T, U> operator+(const std::pair<T, U> &p1, const std::pair<T, U> &p2) {
    return {p1.first + p2.first, p1.second + p2.second};
}
template <typename T, typename U>
std::pair<T, U>& operator-=(std::pair<T, U> &p1, const std::pair<T, U> &p2) {
    p1.first -= p2.first, p1.second -= p2.second;
    return p1;
}
template <typename T, typename U>
std::pair<T, U> operator-(const std::pair<T, U> &p1, const std::pair<T, U> &p2) {
    return {p1.first - p2.first, p1.second - p2.second};
}
template <typename T, typename U, typename V>
std::pair<T, U>& operator*=(std::pair<T, U> &p, const V m) {
    p.first *= m, p.second *= m;
    return p;
}
template <typename T, typename U, typename V>
std::pair<T, U> operator*(const std::pair<T, U> &p, const V m) {
    return {p.first * m, p.second * m};
}
template <typename T, typename U, typename V>
std::pair<T, U> operator*(const V m, const std::pair<T, U> &p) {
    return {p.first * m, p.second * m};
}
} // namespace suisen

using S = pair<int, mint>;

struct FenwickTree1D {
    int N;
    vector<S> BIT;
    FenwickTree1D(int N, S qdef = S{}) : N(N), BIT(N + 1, qdef) {}
    template <class F>
    FenwickTree1D(int N, F f, S qdef = S{}) : FenwickTree1D(N, qdef) {
        for (int i = 1; i <= N; i++) {
            BIT[i] += f();
            int j = i + (i & -i);
            if (j <= N) BIT[j] += BIT[i];
        }
    }
    template <class It>
    FenwickTree1D(It st, It en, S qdef = S{}) : FenwickTree1D(en - st, [&] { return *st++; }, qdef) {}
    vector<S> values() {
        vector<S> ret(BIT.begin() + 1, BIT.end());
        for (int i = N; i >= 1; i--) {
            int j = i + (i & -i);
            if (j <= N) ret[j - 1] -= ret[i - 1];
        }
        return ret;
    }
    void update(int i, S v) {
        for (i++; i <= N; i += i & -i) BIT[i] += v;
    }
    S query(int r) {
        S ret = BIT[0];
        for (r++; r > 0; r -= r & -r) ret += BIT[r];
        return ret;
    }
    S query(int l, int r) {
        return query(r) - query(l - 1);
    }
};

// add (x, y, v)
// query [x1, x2] x [y1, y2]
struct Query {
    int t, xlo, xhi, ylo, yhi;
    S v;
    Query(int t, int xlo, int xhi, int ylo, int yhi, S v) : t(t), xlo(xlo), xhi(xhi), ylo(ylo), yhi(yhi), v(v) {}
};

void add_point(vector<Query>& queries, int x, int y, S v) { queries.push_back(Query(0, x, x, y, y, v)); }

void add_query(vector<Query>& queries, int l, int d, int r, int u) { queries.push_back(Query(1, l, r, d, u, S{})); }

struct Event {
    int t, x, ylo, yhi;
    S v;
    Event(int t, int x, int ylo, int yhi, S v) : t(t), x(x), ylo(ylo), yhi(yhi), v(v) {}
    bool operator<(const Event& e) const { return make_pair(x, t) < make_pair(e.x, e.t); }
};

vector<S> solve(vector<Query> queries) {
    vector<Event> events;
    events.reserve(queries.size() * 2);
    vector<int> YS;
    YS.reserve(queries.size());
    for (auto&& q : queries)
        if (q.t == 0)
            YS.push_back(q.ylo);
    sort(YS.begin(), YS.end());
    YS.erase(unique(YS.begin(), YS.end()), YS.end());
    int qcnt = 0;
    for (auto&& q : queries) {
        if (q.t == 0)
            q.ylo = lower_bound(YS.begin(), YS.end(), q.ylo) - YS.begin();
        else {
            q.ylo = lower_bound(YS.begin(), YS.end(), q.ylo) - YS.begin();
            q.yhi = int(upper_bound(YS.begin(), YS.end(), q.yhi) - YS.begin()) - 1;
            q.v.first = qcnt++;
            if (q.ylo > q.yhi) q.t = -1;
        }
    }
    vector<S> ans(qcnt);
    FenwickTree1D FT(YS.size());
    function<void(int, int)> rec = [&](int l, int r) {
        if (l == r)
            return;
        int m = l + (r - l) / 2;
        rec(l, m);
        rec(m + 1, r);
        events.clear();
        for (int i = l; i <= m; i++)
            if (queries[i].t == 0)
                events.emplace_back(0, queries[i].xlo, queries[i].ylo, queries[i].ylo, queries[i].v);
        if (events.empty())
            return;
        int curSize = events.size();
        for (int i = m + 1; i <= r; i++)
            if (queries[i].t == 1) {
                events.emplace_back(-1, queries[i].xlo, queries[i].ylo, queries[i].yhi, queries[i].v);
                events.emplace_back(1, queries[i].xhi, queries[i].ylo, queries[i].yhi, queries[i].v);
            }
        if (curSize == int(events.size()))
            return;
        sort(events.begin(), events.end());
        for (auto&& e : events) {
            if (e.t == 0)
                FT.update(e.ylo, e.v);
            else
                ans[e.v.first] += e.t * FT.query(e.ylo, e.yhi);
        }
        for (auto&& e : events)
            if (e.t == 0)
                FT.update(e.ylo, { -e.v.first, -e.v.second });
    };
    if (qcnt > 0)
        rec(0, int(queries.size()) - 1);
    return ans;
}

constexpr int inf = numeric_limits<int>::max() - 10;

int main() {
    input(int, n);
    vector<int> x(n), y(n);
    read(x, y);

    vector<mint> answers;

    loop(2) {
        auto p = Permutation::index_sort(x);
        x = p.permute(x);
        y = p.permute(y);
        
        vector<Query> queries;
        mint ans = 0;
        rep(i, n) {
            int u = x[i] - y[i];
            int v = x[i] + y[i];
            add_query(queries, -inf, -inf, u - 1, v - 1);
            add_point(queries, u, v, { 1, x[i] });
        }
        int i = 0;
        for (auto [num, sum] : solve(queries)) {
            ans += mint(num) * x[i++] - sum;
        }
        answers.push_back(ans * 2);

        x.swap(y);
    }

    print(answers);
    return 0;
}