#pragma region competitive_programming
#ifdef __LOCAL
#define _GLIBCXX_DEBUG
#endif
#pragma GCC optimize("Ofast")
#include<bits/stdc++.h>



#include <cassert>
#include <numeric>
#include <type_traits>

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


#include <utility>

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

namespace atcoder {

namespace internal {

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

struct barrett {
    unsigned int _m;
    unsigned long long im;

    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    unsigned int umod() const { return _m; }

    unsigned int mul(unsigned int a, unsigned int b) const {

        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 long long y = x * _m;
        return (unsigned int)(z - y + (z < y ? _m : 0));
    }
};

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;
}

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);

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};

    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


        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

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);

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;
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal

}  // namespace atcoder


#include <cassert>
#include <numeric>
#include <type_traits>

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


namespace tomo0608 {
    std::istream& operator>>(std::istream& is, atcoder::modint998244353& a) { long long v; is >> v; a = v; return is; }
    std::ostream& operator<<(std::ostream& os, const atcoder::modint998244353& a) { return os << a.val(); }
    std::istream& operator>>(std::istream& is, atcoder::modint1000000007& a) { long long v; is >> v; a = v; return is; }
    std::ostream& operator<<(std::ostream& os, const atcoder::modint1000000007& a) { return os << a.val(); }
    template<int m> std::istream& operator>>(std::istream& is, atcoder::static_modint<m>& a) { long long v; is >> v; a = v; return is; }
    template<int m> std::ostream& operator<<(std::ostream& os, const atcoder::static_modint<m>& a) { return os << a.val(); }
    template<int m> std::istream& operator>>(std::istream& is, atcoder::dynamic_modint<m>& a) { long long v; is >> v; a = v; return is; }
    template<int m> std::ostream& operator<<(std::ostream& os, const atcoder::dynamic_modint<m>& a) { return os << a.val(); }

    // Binomial Coefficient of modint
    template<class mint> struct BiCoef {
        std::vector<mint> fact_, inv_, finv_;
        int MAX_SIZE;
        constexpr BiCoef() {}
        constexpr BiCoef(int n) noexcept : MAX_SIZE(n+1), fact_(n+1, 1), inv_(n+1, 1), finv_(n+1, 1) {
            init(n+1);
        }
        constexpr void init(int n) noexcept {
            assert(n >= 1 && n < (int)1e8);
            fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
            int MOD = fact_[0].mod();
            for (int i = 2; i < n; i++) {
                fact_[i] = fact_[i - 1] * i;
                inv_[i] = -inv_[MOD % i] * (MOD / i);
                finv_[i] = finv_[i - 1] * inv_[i];
            }
        }
        constexpr mint com(long long n, long long k) const noexcept {
            if (n < k || n < 0 || k < 0)return 0;
            if(n >= MAX_SIZE)return com_naive(n, k);
            return fact_[n] * finv_[k] * finv_[n - k];
        }
        constexpr mint perm(int n, int k) const noexcept {
            if (n < k || n < 0 || k < 0)return 0;
            return fact_[n] * finv_[n - k];
        }
        constexpr mint homo(int n, int r) { // The number of cases where k indistinguishable balls are put into n distinct boxes
            if (n < 0 || r < 0)return 0;
            return r == 0 ? 1 : com(n + r - 1, r);
        }
        constexpr mint second_stirling_number(int n, int r) { // The number of cases where n distinct balls are put into k indistinguishable boxes, with at least one ball in each box
            mint ret = 0;
            for (int i = 0; i <= r; i++) {
                mint tmp = com(r, i) * mint(i).pow(n);
                ret += ((r - i) & 1) ? -tmp : tmp;
            }
            return ret * finv_[r];
        }
        constexpr mint bell_number(int n, int r) { // The number of cases where n distinct balls are put into k indistinguishable boxes
            if (n == 0) return 1;
            r = std::min(r, n);
            std::vector<mint> pref(r + 1);
            pref[0] = 1;
            for (int i = 1; i <= r; i++) {
                if (i & 1) {
                    pref[i] = pref[i - 1] - finv_[i];
                }
                else {
                    pref[i] = pref[i - 1] + finv_[i];
                }
            }
            mint ret = 0;
            for (int i = 1; i <= r; i++) ret += mint(i).pow(n) * fact_[i] * pref[r - i];
            return ret;
        }

        constexpr mint fact(int n) const noexcept {
            if (n < 0)return 0;
            return fact_[n];
        }
        constexpr mint inv(int n) const noexcept {
            if (n < 0)return 0;
            return inv_[n];
        }
        constexpr mint finv(int n) const noexcept {
            if (n < 0)return 0;
            return finv_[n];
        }
        inline mint operator()(long long n, long long k) { return com(n, k); }

        constexpr mint com_naive(long long n, long long k) {
            if (n < k || n < 0 || k < 0)return 0;
            mint res = 1;
            k = std::min(k, n - k);
            for (int i = 1; i <= k; i++)res *= inv(i) * (n--);
            return res;
        }
    };

} // namespace tomo0608
//typedef atcoder::modint1000000007 mint;
typedef atcoder::modint998244353 mint;
//#include<atcoder/convolution>
//#include "Formal_Power_Series.hpp"
//typedef tomo0608::Formal_Power_Series<mint> fps;

#include <algorithm>
#include <cassert>
#include <vector>

namespace atcoder {

struct dsu {
  public:
    dsu() : _n(0) {}
    explicit dsu(int n) : _n(n), parent_or_size(n, -1) {}

    int merge(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        int x = leader(a), y = leader(b);
        if (x == y) return x;
        if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
        parent_or_size[x] += parent_or_size[y];
        parent_or_size[y] = x;
        return x;
    }

    bool same(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        return leader(a) == leader(b);
    }

    int leader(int a) {
        assert(0 <= a && a < _n);
        if (parent_or_size[a] < 0) return a;
        return parent_or_size[a] = leader(parent_or_size[a]);
    }

    int size(int a) {
        assert(0 <= a && a < _n);
        return -parent_or_size[leader(a)];
    }

    std::vector<std::vector<int>> groups() {
        std::vector<int> leader_buf(_n), group_size(_n);
        for (int i = 0; i < _n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(_n);
        for (int i = 0; i < _n; i++) {
            result[i].reserve(group_size[i]);
        }
        for (int i = 0; i < _n; i++) {
            result[leader_buf[i]].push_back(i);
        }
        result.erase(
            std::remove_if(result.begin(), result.end(),
                           [&](const std::vector<int>& v) { return v.empty(); }),
            result.end());
        return result;
    }

  private:
    int _n;
    std::vector<int> parent_or_size;
};

}  // namespace atcoder



namespace tomo0608 {
    typedef long long ll;
    typedef long double ld;
    template <class T> using V = std::vector<T>;
    template <class T> using VV = V<V<T>>;
    template <class T> using VVV = V<VV<T>>;
    typedef std::pair<int, int> pii;
    typedef std::pair<long long, long long> pll;
    template<class... T>void input(T&... a) { (std::cin >> ... >> a); };

#define INT(...) int __VA_ARGS__; IN(__VA_ARGS__)
#define LL(...) long long __VA_ARGS__; IN(__VA_ARGS__)
#define CHAR(...) char __VA_ARGS__; IN(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; IN(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__; IN(__VA_ARGS__)
#define VEC(type, name, size) std::vector<type> name(size);IN(name)
#define VECVEC(type, name, h, w) std::vector<std::vector<type>> name(h, std::vector<type>(w));IN(name)
    template<class T1, class T2> std::istream& operator>>(std::istream& is, std::pair<T1, T2>& p) { is >> p.first >> p.second; return is; }
    template<class T1, class T2> std::ostream& operator<<(std::ostream& os, const std::pair<T1, T2>& p) { os << '(' << p.first << ", " << p.second << ')'; return os; }
    template<class T> std::istream& operator>>(std::istream& is, std::vector<T>& v) { for (auto& e : v) is >> e; return is; }
    template<class T> std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) { for (auto& e : v) os << e << ' '; return os; }
    template<typename T> std::ostream& operator << (std::ostream& os, std::set<T>& set_var) { os << "{"; for (auto itr = set_var.begin(); itr != set_var.end(); itr++) { os << *itr;++itr;if (itr != set_var.end()) os << ", ";itr--; }os << "}";return os; }
    template <typename T, typename U> std::ostream& operator<<(std::ostream& os, std::map<T, U>& map_var) { os << "{";for (auto itr = map_var.begin(); itr != map_var.end(); itr++) { os << *itr;itr++;if (itr != map_var.end()) os << ", ";itr--; }os << "}";return os; }
    template<int i, class T> void print_tuple(std::ostream&, const T&) {}
    template<int i, class T, class H, class ...Args> void print_tuple(std::ostream& os, const T& t) {
        if (i){os << ", ";} os << std::get<i>(t); print_tuple<i + 1, T, Args...>(os, t);
    }
    template<class ...Args> std::ostream& operator<<(std::ostream& os, const std::tuple<Args...>& t) {
        os << "{"; print_tuple<0, std::tuple<Args...>, Args...>(os, t); return os << "}";
    }

    void IN() {}
    template <class Head, class... Tail> void IN(Head& head, Tail &...tail) {
        std::cin >> head;
        IN(tail...);
    }
    void print() { std::cout << '\n'; }
    template<class T, class... Ts>void print(const T& a, const Ts&... b) { std::cout << a; (std::cout << ... << (std::cout << ' ', b)); std::cout << '\n'; }
    void drop() { std::cout << '\n';exit(0); }
    template<class T, class... Ts>void drop(const T& a, const Ts&... b) { std::cout << a; (std::cout << ... << (std::cout << ' ', b)); std::cout << '\n';exit(0); }
#ifdef __LOCAL
    void debug_out() { std::cerr << std::endl; }
    template < class Head, class... Tail> void debug_out(Head H, Tail... T) { std::cerr << ' ' << H; debug_out(T...); }
#define debug(...) std::cerr << 'L' << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) std::cerr << 'L' << __LINE__ << " " << #x << " = " << (x) << std::endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif


#define rep1(a)          for(long long i = 0; i < (a); i++)
#define rep2(i, a)       for(long long i = 0; i < (a); i++)
#define rep3(i, a, b)    for(long long i = (a); i < (b); i++)
#define rep4(i, a, b, c) for(long long i = (a); i < (b); i += (c))
#define drep1(a)          for(long long i = (a)-1; i >= 0; i--)
#define drep2(i, a)       for(long long i = (a)-1; i >= 0; i--)
#define drep3(i, a, b)    for(long long i = (a)-1; i >= (b); i--)
#define drep4(i, a, b, c) for(long long i = (a)-1; i >= (b); i -= (c))
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define drep(...) overload4(__VA_ARGS__, drep4, drep3, drep2, drep1)(__VA_ARGS__)
#define endl '\n'

    struct io_setup {
        io_setup() {
            std::cin.tie(0);
            std::ios_base::sync_with_stdio(false);
            std::cout << std::setprecision(20);
        }
    }io_setup;
} // namespace tomo0608

namespace tomo0608 {
#define ALL(x) x.begin(),x.end()
    template <class T = long long, class S> T SUM(const S& v) { return accumulate(ALL(v), T(0)); }
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define SORT(v) sort(ALL(v))
#define REVERSE(v) reverse(ALL(v))
#define RSORT(v) sort(ALL(v)); reverse(ALL(v))
#define UNIQUE(x) SORT(x), x.erase(unique(ALL(x)), x.end())
#define lb(c, x) distance((c).begin(), lower_bound(ALL(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(ALL(c), (x)))
    template <typename T> void zip(std::vector<T>& x) { std::vector<T> y = x;UNIQUE(y);for (int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); } }
    template<class T> using priority_queue_rev = std::priority_queue<T, std::vector<T>, std::greater<T>>;
    template<class T, class U> inline bool chmax(T& a, const U& b) { if (a < b) { a = b; return 1; } return 0; }
    template<class T, class U> inline bool chmin(T& a, const U& b) { if (a > b) { a = b; return 1; } return 0; }
    template<class T> inline int count_between(std::vector<T>& a, T l, T r) { return lower_bound(ALL(a), r) - lower_bound(ALL(a), l); } // [l, r)
    template<typename T> int bittest(T n, int k) { return (n >> k) & 1; }
    int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
    int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
    int lowbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
    int lowbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
#define perm(v) for(bool permrepflag = true; (permrepflag ? exchange(permrepflag, false) : next_permutation(ALL(v)));)
    template <typename T, typename S> T ceil(T x, S y) {
        assert(y);
        return (y < 0 ? ceil(-x, -y) : (x > 0 ? (x + y - 1) / y : x / y));
    }

    template <typename T, typename S> T floor(T x, S y) {
        assert(y);
        return (y < 0 ? floor(-x, -y) : (x > 0 ? x / y : x / y - (x % y == 0 ? 0 : 1)));
    }

    template <typename T> std::vector<int> id_sort(const std::vector<T>& v, bool greater = false) {
        int n = v.size();
        std::vector<int> ret(n);
        std::iota(ALL(ret), 0);
        std::sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
        return ret;
    }
}
using namespace atcoder;
using namespace std;
using namespace tomo0608;
int dx[8] = { 1, 0, -1, 0, 1, 1, -1, -1 };
int dy[8] = { 0, 1, 0, -1, 1, -1, -1, 1 };



// インタラクティブ問題のときは出力するたびにcout.flush();を忘れない!!!!!

void solve();
int main() {
    int codeforces = 1;
    //cin >> codeforces;
    while (codeforces--) {
        solve();
    }
    return 0;
}
#pragma endregion

void solve() {
    INT(n, m);
    VEC(ll, a, n);
    dsu uf(n);
    rep(i, m){
        INT(u, v);
        uf.merge(--u, --v);
    }
    mint ans = 1;
    auto g = uf.groups();
    for(auto &comp: g){
        mint tmp = 0;
        for(auto c: comp)tmp += a[c];
        ans *= tmp.pow(comp.size());
    }
    print(ans);
}