// line 1 "answer.cpp"
#if !__INCLUDE_LEVEL__
#include __FILE__
int main() {
    ll n,m;
    input(n,m);
    using mint = modint998244353;
    vl pos(n, -1);
    vl a(n, -1);
    lseg_add_radd<ll> seg(n-m);
    rep(i, m) {
        ll pi, ki;
        input(pi,ki);
        --ki; --pi;
        a[ki] = pi;
        pos[pi] = ki;
    }
    vl ai, ai2;
    rep(i, n) {
        if(a[i]!= -1) ai.push_back(a[i]);
    }
    debug(ai);
    mint ans = inversion_number(ai);
    mint fact = 1;
    rep(i, 1, n-m+1) fact *= i;
    ans *= fact;
    fact = 1;
    rep(i, 1, n-m) fact *= i;
    Combination<mint> comb(100000);
    mint ti = 1;
    rep(i, 1, n-m-1) ti *= i;
    ti *= comb(n-m, 2);
    ti *= comb(n-m, 2);
    ans += ti;
    debug(pos);
    ll c = 0;
    rep(i, n) {
        if (a[i] != -1) {
            pos[a[i]] -= c;
            c++;
        }
    }
    debug(pos);
    rep(i, n) {
        if (pos[i] != -1) {
            seg.apply(0, pos[i], 1);
        }
    }
    debug(fact);
    debug(seg);
    debug(ans);
    rep(i, n-1, -1, -1) {
        if (pos[i] != -1) {
            seg.apply(0, pos[i], -1);
        } else {
            mint ti = mint(seg.all_prod().value);
            ti *= fact;
            ans += ti;
        }
        debug(seg);
    }
    rep(i, n-1, -1, -1) {
        if (pos[i] != -1) {
            seg.apply(pos[i], seg.n(), 1);
        } else {
            mint ti = mint(seg.all_prod().value);
            ti *= fact;
            ans += ti;
        }
        debug(seg);
    }
    print(ans);
}
#else
// line 2 "/Users/seekworser/.cpp_lib/competitive_library/competitive/std/std.hpp"
#include <bits/stdc++.h>
#ifndef LOCAL_TEST
#pragma GCC target ("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#endif // LOCAL_TEST
using namespace std;
// 型名の短縮
using ll = long long;
using pii = pair<int, int>; using pll = pair<ll, ll>;
using vi = vector<int>;  using vvi = vector<vi>; using vvvi = vector<vvi>;
using vl = vector<ll>;  using vvl = vector<vl>; using vvvl = vector<vvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
using vs = vector<string>; using vvs = vector<vector<string>>; using vvvs = vector<vector<vector<string>>>;
template<typename T> vector<vector<T>> vv(int h, int w, T val = T()) { return vector(h, vector<T>(w, val)); }
template<typename T> vector<vector<vector<T>>> vvv(int h1, int h2, int h3, T val = T()) { return vector(h1, vector(h2, vector<T>(h3, val))); }
template<typename T> vector<vector<vector<vector<T>>>> vvvv(int h1, int h2, int h3, int h4, T val = T()) { return vector(h1, vector(h2, vector(h3, vector<T>(h4, val)))); }
template <class T> using priority_queue_min = priority_queue<T, vector<T>, greater<T>>;
// 定数の定義
constexpr double PI = 3.14159265358979323;
constexpr int INF = 100100111; constexpr ll INFL = 3300300300300300491LL;
float EPS = 1e-8; double EPSL = 1e-16;
template<typename T> bool eq(const T x, const T y) { return x == y; }
template<> bool eq<double>(const double x, const double y) { return abs(x - y) < EPSL; }
template<> bool eq<float>(const float x, const float y) { return abs(x - y) < EPS; }
template<typename T> bool neq(const T x, const T y) { return !(eq<T>(x, y)); }
template<typename T> bool ge(const T x, const T y) { return (eq<T>(x, y) || (x > y)); }
template<typename T> bool le(const T x, const T y) { return (eq<T>(x, y) || (x < y)); }
template<typename T> bool gt(const T x, const T y) { return !(le<T>(x, y)); }
template<typename T> bool lt(const T x, const T y) { return !(ge<T>(x, y)); }
constexpr int MODINT998244353 = 998244353;
constexpr int MODINT1000000007 = 1000000007;
// 入出力高速化
struct Nyan { Nyan() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } nyan;
// 汎用マクロの定義
#define all(a) (a).begin(), (a).end()
#define sz(x) ((ll)(x).size())
#define rep1(n) for(ll dummy_iter = 0LL; dummy_iter < n; ++dummy_iter) // 0 から n-1 まで昇順
#define rep2(i, n) for(ll i = 0LL, i##_counter = 0LL; i##_counter < ll(n); ++(i##_counter), (i) = i##_counter) // 0 から n-1 まで昇順
#define rep3(i, s, t) for(ll i = ll(s), i##_counter = ll(s); i##_counter < ll(t); ++(i##_counter), (i) = (i##_counter)) // s から t まで昇順
#define rep4(i, s, t, step) for(ll i##_counter = step > 0 ? ll(s) : -ll(s), i##_end = step > 0 ? ll(t) : -ll(t), i##_step = abs(step), i = ll(s); i##_counter < i##_end; i##_counter += i##_step, i = step > 0 ? i##_counter : -i##_counter) // s から t まで stepずつ
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define repe(a, v) for(auto& a : (v)) // v の全要素（変更可能）
#define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod
#define sdiv(n, m) (((n) - smod(n, m)) / (m)) // 非負div
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去
int Yes(bool b=true) { cout << (b ? "Yes\n" : "No\n"); return 0; };
int YES(bool b=true) { cout << (b ? "YES\n" : "NO\n"); return 0; };
int No(bool b=true) {return Yes(!b);};
int NO(bool b=true) {return YES(!b);};
template<typename T, size_t N> T max(array<T, N>& a) { return *max_element(all(a)); };
template<typename T, size_t N> T min(array<T, N>& a) { return *min_element(all(a)); };
template<typename T> T max(vector<T>& a) { return *max_element(all(a)); };
template<typename T> T min(vector<T>& a) { return *min_element(all(a)); };
template<typename T> vector<T> vec_slice(const vector<T>& a, int l, int r) { vector<T> rev; rep(i, l, r) rev.push_back(a[i]); return rev; };
template<typename T> T sum(vector<T>& a, T zero = T(0)) { T rev = zero; rep(i, sz(a)) rev += a[i]; return rev; };
template<typename T> bool in_range(const T& val, const T& s, const T& t) { return s <= val && val < t; };

template <class T> inline vector<T>& operator--(vector<T>& v) { repe(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repe(x, v) ++x; return v; }

// modでのpow
ll powm(ll a, ll n, ll mod=INFL) {
    ll res = 1;
    while (n > 0) {
        if (n & 1) res = (res * a) % mod;
        if (n > 1) a = (a * a) % mod;
        n >>= 1;
    }
    return res;
}
// 整数Sqrt
ll sqrtll(ll x) {
    assert(x >= 0);
    ll rev = sqrt(x);
    while(rev * rev > x) --rev;
    while((rev+1) * (rev+1)<=x) ++rev;
    return rev;
}
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新（更新されたら true を返す）
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新（更新されたら true を返す）
int digit(ll x, int d=10) { int rev=0; while (x > 0) { rev++; x /= d;}; return rev; } // xのd進数桁数
/**
 * @brief std.hpp
 * @docs docs/std/std.md
 */
// line 6 "/Users/seekworser/.cpp_lib/competitive_library/atcoder/lazysegtree.hpp"

// line 2 "/Users/seekworser/.cpp_lib/competitive_library/atcoder/internal_bit.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
constexpr int bsf_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

}  // namespace internal

}  // namespace atcoder
// line 8 "/Users/seekworser/.cpp_lib/competitive_library/atcoder/lazysegtree.hpp"

namespace atcoder {

template <class S,
          S (*_op)(S, S),
          S (*_e)(),
          class F,
          S (*_mapping)(F, S),
          F (*_composition)(F, F),
          F (*_id)()>
struct lazy_segtree {
  public:
    S (*op)(S, S) = _op;
    S (*e)() = _e;
    S (*mapping)(F, S) = _mapping;
    F (*composition)(F, F) = _composition;
    F (*id)() = _id;
    lazy_segtree() : lazy_segtree(0) {}
    explicit lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, _e())) {}
    explicit lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = internal::ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        lz = std::vector<F>(size, id());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    void add(int p, S x) {
        assert(0 <= p && p < _n);
        (*this).set(p, (*this).get(p) + x);
    }

    S get(int p) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return d[p];
    }

    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return e();

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        S sml = e(), smr = e();
        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }

        return op(sml, smr);
    }

    S all_prod() { return d[1]; }

    void apply(int p, F f) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = mapping(f, d[p]);
        for (int i = 1; i <= log; i++) update(p >> i);
    }
    void apply(int l, int r, F f) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return;

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while (l < r) {
                if (l & 1) all_apply(l++, f);
                if (r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }

        for (int i = 1; i <= log; i++) {
            if (((l >> i) << i) != l) update(l >> i);
            if (((r >> i) << i) != r) update((r - 1) >> i);
        }
    }

    template <bool (*g)(S)> int max_right(int l) {
        return max_right(l, [](S x) { return g(x); });
    }
    template <class G> int max_right(int l, G g) {
        assert(0 <= l && l <= _n);
        assert(g(e()));
        if (l == _n) return _n;
        l += size;
        for (int i = log; i >= 1; i--) push(l >> i);
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!g(op(sm, d[l]))) {
                while (l < size) {
                    push(l);
                    l = (2 * l);
                    if (g(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*g)(S)> int min_left(int r) {
        return min_left(r, [](S x) { return g(x); });
    }
    template <class G> int min_left(int r, G g) {
        assert(0 <= r && r <= _n);
        assert(g(e()));
        if (r == 0) return 0;
        r += size;
        for (int i = log; i >= 1; i--) push((r - 1) >> i);
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!g(op(d[r], sm))) {
                while (r < size) {
                    push(r);
                    r = (2 * r + 1);
                    if (g(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

    int n() {return (*this)._n;}

  private:
    int _n, size, log;
    std::vector<S> d;
    std::vector<F> lz;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
    void all_apply(int k, F f) {
        d[k] = mapping(f, d[k]);
        if (k < size) lz[k] = composition(f, lz[k]);
    }
    void push(int k) {
        all_apply(2 * k, lz[k]);
        all_apply(2 * k + 1, lz[k]);
        lz[k] = id();
    }
};

}  // namespace atcoder
// line 4 "/Users/seekworser/.cpp_lib/competitive_library/competitive/data_structure/lazysegtree.hpp"
template <typename S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()>
std::ostream& operator<<(std::ostream& os, atcoder::lazy_segtree<S, op, e, F, mapping, composition, id> seg) {
    int n = seg.n();
    rep(i, n) { os << seg.get(i); if (i != n-1) os << " "; }
    return os;
};

namespace lsegtree_internal {
    template<typename T> struct AddNode {
        T value;
        ll size;
        AddNode() : value(T(0)), size(1) {};
        AddNode(T value, ll size) : value(value), size(size) {};
        friend ostream& operator<<(std::ostream& os, const AddNode<T> &n) { os << n.value; return os; };
    };

    template<typename T> T e_max() { return -INFL; }
    template<> int e_max() { return -INF; }
    template<typename T> T e_min() { return INFL; }
    template<> int e_min() { return INF; }
    template<typename T> AddNode<T> e_add() { return {0, 1}; }

    template<typename T> T op_max(T x, T y) { return x > y ? x : y; }
    template<typename T> T op_min(T x, T y) { return x < y ? x : y; }
    template<typename T> AddNode<T> op_add(AddNode<T> x, AddNode<T> y) { return {x.value + y.value, x.size + y.size}; }

    template<typename T> T id_radd(){ return 0; }
    template<typename T> T id_rupdate(){ return INFL; }
    template<> int id_rupdate(){ return INF; }

    template<typename T> AddNode<T> mapping_add_radd(T f, AddNode<T> x){ return {x.value + f * x.size, x.size}; }
    template<typename T> AddNode<T> mapping_add_rupdate(T f, AddNode<T> x){
        AddNode<T> rev = AddNode<T>(x);
        if(f != id_rupdate<T>()) rev.value = f * rev.size;
        return rev;
    }
    template<typename T> T mapping_radd(T f, T x){ return f+x; }
    template<typename T> T mapping_rupdate(T f, T x){ return (f == id_rupdate<T>() ? x : f); }

    template<typename T> T composition_radd(T f, T g){ return f+g; }
    template<typename T> T composition_rupdate(T f, T g){ return (f == id_rupdate<T>() ? g : f); }
}

template <typename S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()>
using lsegtree = atcoder::lazy_segtree<S, op, e, F, mapping, composition, id>;
template<typename T> using lseg_add_radd = atcoder::lazy_segtree<lsegtree_internal::AddNode<T>, lsegtree_internal::op_add<T>, lsegtree_internal::e_add<T>, T, lsegtree_internal::mapping_add_radd<T>, lsegtree_internal::composition_radd<T>, lsegtree_internal::id_radd<T>>;
template<typename T> using lseg_min_radd = atcoder::lazy_segtree<T, lsegtree_internal::op_min<T>, lsegtree_internal::e_min<T>, T, lsegtree_internal::mapping_radd<T>, lsegtree_internal::composition_radd<T>, lsegtree_internal::id_radd<T>>;
template<typename T> using lseg_max_radd = atcoder::lazy_segtree<T, lsegtree_internal::op_max<T>, lsegtree_internal::e_max<T>, T, lsegtree_internal::mapping_radd<T>, lsegtree_internal::composition_radd<T>, lsegtree_internal::id_radd<T>>;
template<typename T> using lseg_add_rupdate = atcoder::lazy_segtree<lsegtree_internal::AddNode<T>, lsegtree_internal::op_add<T>, lsegtree_internal::e_add<T>, T, lsegtree_internal::mapping_add_rupdate<T>, lsegtree_internal::composition_rupdate<T>, lsegtree_internal::id_rupdate<T>>;
template<typename T> using lseg_min_rupdate = atcoder::lazy_segtree<T, lsegtree_internal::op_min<T>, lsegtree_internal::e_min<T>, T, lsegtree_internal::mapping_rupdate<T>, lsegtree_internal::composition_rupdate<T>, lsegtree_internal::id_rupdate<T>>;
template<typename T> using lseg_max_rupdate = atcoder::lazy_segtree<T, lsegtree_internal::op_max<T>, lsegtree_internal::e_max<T>, T, lsegtree_internal::mapping_rupdate<T>, lsegtree_internal::composition_rupdate<T>, lsegtree_internal::id_rupdate<T>>;
/**
 * @brief 遅延セグメント木（ラッパー）
 * @docs docs/data_structure/lazysegtree.md
 */
// line 4 "/Users/seekworser/.cpp_lib/competitive_library/atcoder/modint.hpp"
#include <type_traits>

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

// line 3 "/Users/seekworser/.cpp_lib/competitive_library/atcoder/internal_math.hpp"

#ifdef _MSC_VER
#include <intrin.h>
#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
// line 5 "/Users/seekworser/.cpp_lib/competitive_library/atcoder/internal_type_traits.hpp"

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
// line 12 "/Users/seekworser/.cpp_lib/competitive_library/atcoder/modint.hpp"

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 mint& rhs) { (*this)._v = rhs.val(); return *this; }

    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 mint& rhs) { (*this)._v = rhs.val(); return *this; }

    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
// line 4 "/Users/seekworser/.cpp_lib/competitive_library/competitive/math/modint.hpp"
namespace modint_internal {
    template<typename Mint> Mint pow(Mint a, ll n) {
        Mint res = 1;
        while (n > 0) {
            if (n & 1) res *= a;
            if (n > 1) a *= a;
            n >>= 1;
        }
        return res;
    }
    template<typename Mint> inline istream& input(istream& is, Mint& x) {ll a; is >> a; x = a; return is; }
    template<typename Mint> inline ostream& print(ostream& os, const Mint& x) { os << x.val(); return os; }
}
inline istream& operator>>(istream& is, atcoder::modint& x) { return modint_internal::input(is, x); }
template<int m> inline istream& operator>>(istream& is, atcoder::static_modint<m>& x) { return modint_internal::input(is, x); }
inline ostream& operator<<(ostream& os, const atcoder::modint& x) { return modint_internal::print(os, x); }
template<int m> inline ostream& operator<<(ostream& os, const atcoder::static_modint<m>& x) { return modint_internal::print(os, x); }
atcoder::modint pow(atcoder::modint a, ll n) { return modint_internal::pow(a, n); }
template<int m> atcoder::static_modint<m> pow(atcoder::static_modint<m> a, ll n) { return modint_internal::pow(a, n); }
using modint998244353 = atcoder::modint998244353;
using modint1000000007 = atcoder::modint1000000007;
using modint = atcoder::modint;
/**
 * @brief modint.hpp
 * @docs docs/math/modint.md
 */
// line 3 "/Users/seekworser/.cpp_lib/competitive_library/competitive/data_structure/bit.hpp"
template<typename T> struct Bit {
    vector<T> bit;
    int _n;
    Bit(int size, T val = T(0)) : _n(size), bit(size+1, val) {}
    Bit(const vector<T> val) : _n(sz(val)), bit(sz(val)+1, T(0)) {
        rep(i, _n) set(i, val[i]);
    }
    void add(int p, T x) {
        assert(0 <= p && p <= _n);
        p++;
        for (int i = p; i <= _n; i += i & -i) {
            bit[i] += x;
        }
    }
    T sum(int r) const {
        assert(0 <= r && r <= _n);
        T ret = 0;
        for (int i = r; i > 0; i -= i & -i){
            ret += bit[i];
        }
        return ret;
    }
    T sum(int l, int r) const {
        return sum(r) - sum(l);
    }
    T get(int p) const {
        assert(0 <= p && p < _n);
        return sum(p, p+1);
    }
    void set(int p, T x) {
        assert(0 <= p && p < _n);
        add(p, x - get(p));
    }
    int lower_bound(T w) const {
        if (w <= 0) return 0;
        int x = 0;
        for (int k = 1 << __lg(_n); k; k >>= 1) {
            if (x + k <= _n && bit[x + k] < w) {
                w -= bit[x + k];
                x += k;
            }
        }
        return x;
    }
    int upper_bound(T w) const {
        if (w < 0) return 0;
        int x = 0;
        for (int k = 1 << __lg(_n); k; k >>= 1) {
            if (x + k <= _n && bit[x + k] <= w) {
                w -= bit[x + k];
                x += k;
            }
        }
        return x;
    }
};
template <typename T> std::ostream& operator<<(std::ostream& os, const Bit<T> bit) {
    rep(i, bit._n) { os << bit.get(i); if (i != bit._n-1) os << " "; }
    return os;
};
/**
 * @brief BIT（Binary Index Tree）
 * @docs docs/data_structure/bit.md
 */
// line 4 "/Users/seekworser/.cpp_lib/competitive_library/competitive/math/inversion_num.hpp"
template<class T> ll inversion_number(vector<T> &a) {
    ll ans = 0;
    Bit<ll> b(a.size());
    vector<T> sorted_a = a;
    sort(all(sorted_a));
    unordered_map<T, ll> ind_map;
    rep(i, a.size()) ind_map[sorted_a[i]] = i;
    rep(i, a.size()) {
        ans += i - b.sum(ind_map[a[i]] + 1);
        b.add(ind_map[a[i]], 1);
    }
    return ans;
}
/**
 * @brief inversion_num.hpp
 * @docs docs/math/inversion_num.md
 */
// line 4 "/Users/seekworser/.cpp_lib/competitive_library/competitive/math/combination.hpp"
template<typename mint> struct Combination {
    vector<mint> fact, fact_inv;
    Combination(int nmax) : fact(nmax+1), fact_inv(nmax+1) {
        int p = mint::mod();
        vector<mint> inv(nmax+1);
        fact[0] = fact[1] = 1;
        fact_inv[0] = fact_inv[1] = 1;
        inv[0] = 0;
        inv[1] = 1;
        for (int i = 2; i < nmax+1; i++) {
            fact[i] = fact[i - 1] * i;
            inv[i] = p - inv[p % i] * (p / i);
            fact_inv[i] = fact_inv[i - 1] * inv[i];
        }
    }
    mint operator()(int n, int r) {
        if (r < 0 || n < r) return 0;
        return fact[n] * fact_inv[r] * fact_inv[n - r];
    }
};
/**
 * @brief combination.hpp
 * @docs docs/math/combination.md
 */
// line 3 "/Users/seekworser/.cpp_lib/competitive_library/competitive/std/io.hpp"
// 演算子オーバーロード（プロトタイプ宣言）
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p);
template <class T> inline istream& operator>>(istream& is, vector<T>& v);
template <class T, class U> inline ostream& operator<<(ostream& os, const pair<T, U>& p);
template <class T> inline ostream& operator<<(ostream& os, const vector<T>& v);
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp);
template <typename T> ostream &operator<<(ostream &os, const set<T> &st);
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st);
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &st);
template <typename T> ostream &operator<<(ostream &os, queue<T> q);
template <typename T> ostream &operator<<(ostream &os, deque<T> q);
template <typename T> ostream &operator<<(ostream &os, stack<T> st);
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq);

// 演算子オーバーロード
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repe(x, v) is >> x; return is; }
template <class T, class U> inline ostream& operator<<(ostream& os, const pair<T, U>& p) { os << p.first << " " << p.second; return os; }
template <class T> inline ostream& operator<<(ostream& os, const vector<T>& v) { rep(i, sz(v)) { os << v.at(i); if (i != sz(v) - 1) os << " "; } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp) { for (auto &[key, val] : mp) { os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &st) { ll cnt = 0; for (auto &e : st) { os << e << (++cnt != (int)st.size() ? " " : ""); } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q) { while (q.size()) { os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q) { while (q.size()) { os << q.front() << " "; q.pop_front(); } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st) { while (st.size()) { os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq) { while (pq.size()) { os << pq.top() << " "; pq.pop(); } return os; }

template <typename T> int print_sep_end(string sep, string end, const T& val) { (void)sep; cout << val << end; return 0; };
template <typename T1, typename... T2> int print_sep_end(string sep, string end, const T1 &val, const T2 &...remain) {
    cout << val << sep;
    print_sep_end(sep, end, remain...);
    return 0;
};
template <typename... T> int print(const T &...args) { print_sep_end(" ", "\n", args...); return 0; };
template <typename... T> void flush() { cout << flush; };
template <typename... T> int print_and_flush(const T &...args) { print(args...); flush(); return 0; };
#define debug(...) debug_func(0, #__VA_ARGS__, __VA_ARGS__) // debug print
template <typename T> void input(T &a) { cin >> a; };
template <typename T1, typename... T2> void input(T1&a, T2 &...b) { cin >> a; input(b...); };
#ifdef LOCAL_TEST
template <typename T> void debug_func(int i, const T name) { (void)i; (void)name; cerr << endl; }
template <typename T1, typename T2, typename... T3> void debug_func(int i, const T1 &name, const T2 &a, const T3 &...b) {
    int scope = 0;
    for ( ; (scope != 0 || name[i] != ',') && name[i] != '\0'; i++ ) {
        cerr << name[i];
        if (name[i] == '(' || name[i] == '{') scope++;
        if (name[i] == ')' || name[i] == '}') scope--;
    }
    cerr << ":" << a << " ";
    debug_func(i + 1, name, b...);
}
template <typename T1, typename T2, typename... T3> void debug_func(int i, const T1 &name, T2 &a, T3 &...b) {
    int scope = 0;
    for ( ; (scope != 0 || name[i] != ',') && name[i] != '\0'; i++ ) {
        cerr << name[i];
        if (name[i] == '(' || name[i] == '{') scope++;
        if (name[i] == ')' || name[i] == '}') scope--;
    }
    cerr << ":" << a << " ";
    debug_func(i + 1, name, b...);
}
#endif
#ifndef LOCAL_TEST
template <typename... T>
void debug_func(T &...) {}
template <typename... T>
void debug_func(const T &...) {}
#endif
/**
 * @brief io.hpp
 * @docs docs/std/io.md
 */
// line 80 "answer.cpp"
#endif