#line 1 "library-cpp/other/template.hpp"
// clang-format off
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using i128 = __int128_t;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
template <class T> using maxheap = priority_queue<T>;
template <class T> using minheap = priority_queue<T, vector<T>, greater<T>>;
template <class T> using vec = vector<T>;
template <class T> using vvec = vector<vector<T>>;
#define OVERLOAD_REP(_1, _2, _3, name, ...) name
#define REP0(n) for (auto minato = decay_t<decltype(n)>{}; minato < (n); ++minato)
#define REP1(i, n) for (auto i = decay_t<decltype(n)>{}; (i) < (n); (i)++)
#define REP2(i, l, r) for (auto i = (l); (i) < (r); (i)++)
#define rep(...) OVERLOAD_REP(__VA_ARGS__, REP2, REP1, REP0)(__VA_ARGS__)
#define OVERLOAD_RREP(_1, _2, _3, name, ...) name
#define RREP1(i, n) for (auto i = (n) - 1; (i) >= decay_t<decltype(n)>{}; (i)--)
#define RREP2(i, l, r) for (auto i = (r) - 1; (i) >= (l); (i)--)
#define rrep(...) OVERLOAD_RREP(__VA_ARGS__, RREP2, RREP1)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
template <class Container> int SZ(const Container& v) { return int(v.size()); }
template <class T> void UNIQUE(vector<T>& v) { v.erase(unique(v.begin(), v.end()), v.end()); }
template <class T> T MAX(const vector<T>& v) { return *max_element(v.begin(), v.end()); }
template <class T> T MIN(const vector<T>& v) { return *min_element(v.begin(), v.end()); }
template <class T> T SUM(const vector<T>& v) { return accumulate(v.begin(), v.end(), T(0)); }
template <class T> T ABS(T x) { return max(x, -x); }
long long floor_div(long long n, long long d) { return n / d - ((n ^ d) < 0 && n % d); }
template <class T1, class T2> bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; }
template <class T1, class T2> bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; }
int topbit(ull x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); }
int botbit(ull x) { return x == 0 ? 64 : __builtin_ctzll(x); }
int popcount(ull x) { return __builtin_popcountll(x); }
int kthbit(ull x, int k) { return (x >> k) & 1; }
constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x - 1) * 10; }
template <typename S> void rearrange(const vector<S>& id) { (void)id; }
template <typename S, typename T> void rearrange_exec(const vector<S>& id, vector<T>& v) { vector<T> w(v.size()); for (size_t i = 0; i < id.size(); i++) { w[i] = v[id[i]]; } v.swap(w); }
template <typename S, typename Head, typename... Tail> void rearrange(const vector<S>& id, Head& a, Tail& ...tail) { rearrange_exec(id, a); rearrange(id, tail...); }
istream& operator>>(istream& is, __int128_t& x) {
    x = 0;
    string s;
    is >> s;
    int n = int(s.size()), it = 0;
    if (s[0] == '-') it++;
    for (; it < n; it++) x = (x * 10 + s[it] - '0');
    if (s[0] == '-') x = -x;
    return is;
}
ostream& operator<<(ostream& os, __int128_t x) {
    if (x == 0) return os << 0;
    if (x < 0) os << '-', x = -x;
    deque<int> deq;
    while (x) deq.emplace_front(x % 10), x /= 10;
    for (int e : deq) os << e;
    return os;
}
template <class T> vector<T> &operator++(vector<T>& v) { for (auto& e : v) { e++; } return v;} 
template <class T> vector<T> operator++(vector<T>& v, int) { auto res = v; for (auto& e : v) { e++; } return res; }
template <class T> vector<T> &operator--(vector<T>& v) { for (auto& e : v) { e--; } return v; }
template <class T> vector<T> operator--(vector<T>& v, int) { auto res = v; for (auto& e : v) { e--; } return res; }
template <class T1, class T2> pair<T1, T2> operator-(const pair<T1, T2>& x) { return pair<T1, T2>(-x.first, -x.second); }
template <class T1, class T2> pair<T1, T2> operator-(const pair<T1, T2>& x, const pair<T1, T2>& y) { return pair<T1, T2>(x.first - y.first, x.second - y.second); }
template <class T1, class T2> pair<T1, T2> operator+(const pair<T1, T2>& x, const pair<T1, T2>& y) { return pair<T1, T2>(x.first + y.first, x.second + y.second); }
template <class T1, class T2> pair<T1, T2> operator+=(pair<T1, T2>& l, const pair<T1, T2>& r) { return l = l + r; }
template <class T1, class T2> pair<T1, T2> operator-=(pair<T1, T2>& l, const pair<T1, T2>& r) { return l = l - r; }
constexpr char ln = '\n';
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
void YES(bool t = true) { cout << YESNO[t] << "\n"; }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = true) { cout << YesNo[t] << "\n"; }
void No(bool t = 1) { Yes(!t); }
template <class T> void drop(T x) { cout << x << "\n"; exit(0); }
#define INT(...)     \
    int __VA_ARGS__; \
    IN(__VA_ARGS__)
#define LL(...)     \
    ll __VA_ARGS__; \
    IN(__VA_ARGS__)
#define STR(...)        \
    string __VA_ARGS__; \
    IN(__VA_ARGS__)
#define CHR(...)      \
    char __VA_ARGS__; \
    IN(__VA_ARGS__)
#define LDB(...)             \
    long double __VA_ARGS__; \
    IN(__VA_ARGS__)
#define VEC(type, name, size) \
    vector<type> name(size);  \
    IN(name)
#define VEC2(type, name1, name2, size)     \
    vector<type> name1(size), name2(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i])
#define VEC3(type, name1, name2, name3, size)           \
    vector<type> name1(size), name2(size), name3(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i])
#define VEC4(type, name1, name2, name3, name4, size)                 \
    vector<type> name1(size), name2(size), name3(size), name4(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i], name4[i]);
#define VV(type, name, N, M)                       \
    vector<vector<type>> name(N, vector<type>(M)); \
    IN(name)
template <class T> void scan(T& a) { cin >> a; }
template <class T> void scan(vector<T>& a) { for (auto& i : a) scan(i); }
void IN() {}
template <class Head, class... Tail> void IN(Head& head, Tail&... tail) { scan(head); IN(tail...); }
std::vector<std::vector<int>> read_graph(int N, int M) {
    std::vector<std::vector<int>> g(N);
    for (int i = 0; i < M; i++) {
        int a, b;
        cin >> a >> b;
        a--, b--;
        g[a].emplace_back(b);
        g[b].emplace_back(a);
    }
    return g;
}
std::vector<std::vector<int>> read_tree(int N) { return read_graph(N, N - 1); }
void print() { cout << "\n"; }
template <class T> void print(const vector<T>& v) { for (auto it = v.begin(); it != v.end(); ++it) { if (it != v.begin()) { cout << " "; } cout << *it; } print(); }
template <class T, class... Args> void print(const T& x, const Args& ... args) { cout << x; if (sizeof...(Args)) cout << " "; print(args...); }
#ifdef MINATO_LOCAL
template <class T1, class T2> ostream& operator<<(ostream& os, pair<T1, T2> p);
template <class ...Args> ostream& operator<<(ostream& os, tuple<Args...> t);
template <class T> ostream& operator<<(ostream& os, vector<T> v);
template <class T, size_t N> ostream& operator<<(ostream& os, array<T, N> a);
template <class T, size_t N> enable_if_t<!is_same_v<char, remove_cv_t<T>>, ostream>& operator<<(ostream& os, T(&a)[N]);
template <class Key> ostream& operator<<(ostream& os, set<Key> s);
template <class Key, class T> ostream& operator<<(ostream& os, map<Key, T> mp);
template <class Key> ostream& operator<<(ostream& os, multiset<Key> s);
template <class T> ostream& operator<<(ostream& os, queue<T> q);
template <class T> ostream& operator<<(ostream& os, deque<T> q);
template <class T> ostream& operator<<(ostream& os, priority_queue<T> q);
template <class T> ostream& operator<<(ostream& os, priority_queue<T, vector<T>, greater<T>> q);
template <class T1, class T2> ostream& operator<<(ostream& os, pair<T1, T2> p) { return os << "(" << p.first << ", " << p.second << ")"; }
template <size_t N, class TUPLE> void debug_tuple(ostream& os, TUPLE _) { (void)os; (void)_; }
template <size_t N, class TUPLE, class T, class ...Args> void debug_tuple(ostream &os, TUPLE t) { os << (N == 0 ? "" : ", ") << get<N>(t); debug_tuple<N + 1, TUPLE, Args...>(os, t); }
template <class ...Args> ostream& operator<<(ostream& os, tuple<Args...> t) { os << "("; debug_tuple<0, tuple<Args...>, Args...>(os, t); return os << ")"; }
string debug_delim(int& i) { return i++ == 0 ? "" : ", "; }
#define debug_embrace(x) { int i = 0; os << "{";  { x } return os << "}"; }
template <class T> ostream& operator<<(ostream& os, vector<T> v) { debug_embrace( for (T e : v) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> ostream& operator<<(ostream& os, array<T, N> a) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> enable_if_t<!is_same_v<char, remove_cv_t<T>>, ostream>& operator<<(ostream& os, T(&a)[N]) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class Key> ostream& operator<<(ostream& os, set<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class Key, class T> ostream& operator<<(ostream& os, map<Key, T> mp) { debug_embrace( for (auto e : mp) { os << debug_delim(i) << e; }) }
template <class Key> ostream& operator<<(ostream& os, multiset<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class T> ostream& operator<<(ostream& os, queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.front(); } ) }
template <class T> ostream& operator<<(ostream& os, deque<T> q) { debug_embrace( for (T e : q) { os << debug_delim(i) << e; } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T, vector<T>, greater<T>> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) }
void debug_out() { cerr << endl; }
template <class T, class... Args> void debug_out(const T& x, const Args& ... args) { cerr << " " << x; debug_out(args...); }
#define debug(...) cerr << __LINE__ << " : [" << #__VA_ARGS__ << "] =", debug_out(__VA_ARGS__)
#else
#define debug(...) (void(0))
#endif
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// clang-format on
#line 2 "library-cpp/segmenttree/SegmentTree.hpp"

#line 5 "library-cpp/segmenttree/SegmentTree.hpp"

template <class T, class F> struct SegmentTree {
  private:
    F op;
    T e;
    int _n, size_, log;
    std::vector<T> node;

  public:
    SegmentTree() {
    }
    SegmentTree(const F& op, T e, int n)
        : SegmentTree(op, e, std::vector<T>(n, e)) {
    }
    SegmentTree(const F& op, T e, const std::vector<T>& v)
        : op(op), e(e), _n(int(v.size())), log(0) {
        while ((1 << log) < _n) log++;
        size_ = 1 << log;
        node = std::vector<T>(2 * size_, e);
        for (int i = 0; i < _n; i++) node[size_ + i] = v[i];
        for (int i = size_ - 1; i >= 1; i--) {
            update(i);
        }
    }

    int size() const {
        return _n;
    }

    // (0-indexed)
    void set(int p, T x) {
        assert(0 <= p && p < _n);
        p += size_;
        node[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    // [l, r) (0-indexed)
    T get(int l, int r) {
        if (l >= r) return e;
        T resl = e, resr = e;
        l += size_;
        r += size_;
        while (l < r) {
            if (l & 1) resl = op(resl, node[l++]);
            l >>= 1;
            if (r & 1) resr = op(node[--r], resr);
            r >>= 1;
        }
        return op(resl, resr);
    }

    T all_get() {
        return node[1];
    }

    template <class C> int max_right(int l, const C& check) {
        assert(0 <= l && l <= _n);
        assert(check(e));
        if (l == _n) return _n;
        l += size_;
        T sm = e;
        do {
            while (~l & 1) l >>= 1;
            if (!check(op(sm, node[l]))) {
                while (l < size_) {
                    l = (2 * l);
                    if (check(op(sm, node[l]))) {
                        sm = op(sm, node[l]);
                        l++;
                    }
                }
                return l - size_;
            }
            sm = op(sm, node[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <class C> int min_left(int r, const C& check) {
        assert(0 <= r && r <= _n);
        assert(check(e));
        if (r == 0) return 0;
        r += size_;
        T sm = e;
        do {
            r--;
            while (r > 1 && (r & 1)) r >>= 1;
            if (!check(op(node[r], sm))) {
                while (r < size_) {
                    r = (2 * r + 1);
                    if (check(op(node[r], sm))) {
                        sm = op(node[r], sm);
                        r--;
                    }
                }
                return r + 1 - size_;
            }
            sm = op(node[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

    T operator[](int p) {
        assert(0 <= p && p < _n);
        return node[p + size_];
    }

#ifdef MINATO_LOCAL
    friend ostream& operator<<(ostream& os, SegmentTree r) {
        std::vector<T> v(r.size());
        for (int i = 0; i < r.size(); i++) {
            v[i] = r[i];
        }
        os << v;
        return os;
    }
#endif

  private:
    void update(int k) {
        node[k] = op(node[2 * k], node[2 * k + 1]);
    }
};

template <typename T> auto buildPointSetRangeMin(int n, T e) {
    auto f = [](T a, T b) { return min(a, b); };
    SegmentTree seg(f, e, n);
    return seg;
}

template <typename T> auto buildPointSetRangeMin(const std::vector<T>& v, T e) {
    auto f = [](T a, T b) { return min(a, b); };
    SegmentTree seg(f, e, v);
    return seg;
}

template <typename T> auto buildPointSetRangeMax(int n, T e) {
    auto f = [](T a, T b) { return max(a, b); };
    SegmentTree seg(f, e, n);
    return seg;
}

template <typename T> auto buildPointSetRangeMax(const std::vector<T>& v, T e) {
    auto f = [](T a, T b) { return max(a, b); };
    SegmentTree seg(f, e, v);
    return seg;
}
#line 2 "library-cpp/mod/ModInt.hpp"

#line 2 "library-cpp/other/type_traits.hpp"

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
#line 4 "library-cpp/mod/ModInt.hpp"

#line 6 "library-cpp/mod/ModInt.hpp"

template <int m> struct ModInt {
  public:
    static constexpr int mod() {
        return m;
    }
    static ModInt raw(int v) {
        ModInt x;
        x._v = v;
        return x;
    }

    ModInt() : _v(0) {
    }

    template <class T, internal::is_signed_int_t<T>* = nullptr> 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> ModInt(T v) {
        _v = (unsigned int)(v % umod());
    }

    unsigned int val() const {
        return _v;
    }

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

    ModInt& operator+=(const ModInt& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    ModInt& operator-=(const ModInt& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    ModInt& operator*=(const ModInt& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    ModInt& operator^=(long long n) {
        ModInt x = *this;
        *this = 1;
        if (n < 0) x = x.inv(), n = -n;
        while (n) {
            if (n & 1) *this *= x;
            x *= x;
            n >>= 1;
        }
        return *this;
    }
    ModInt& operator/=(const ModInt& rhs) {
        return *this = *this * rhs.inv();
    }

    ModInt operator+() const {
        return *this;
    }
    ModInt operator-() const {
        return ModInt() - *this;
    }
    explicit operator bool() const {
        return _v != 0;
    }

    ModInt pow(long long n) const {
        ModInt r = *this;
        r ^= n;
        return r;
    }
    ModInt inv() const {
        int a = _v, b = umod(), y = 1, z = 0, t;
        for (;;) {
            t = a / b;
            a -= t * b;
            if (a == 0) {
                assert(b == 1 || b == -1);
                return ModInt(b * z);
            }
            y -= t * z;
            t = b / a;
            b -= t * a;
            if (b == 0) {
                assert(a == 1 || a == -1);
                return ModInt(a * y);
            }
            z -= t * y;
        }
    }

    friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) += rhs;
    }
    friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) -= rhs;
    }
    friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) *= rhs;
    }
    friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) /= rhs;
    }
    friend ModInt operator^(const ModInt& lhs, long long rhs) {
        return ModInt(lhs) ^= rhs;
    }
    friend bool operator==(const ModInt& lhs, const ModInt& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const ModInt& lhs, const ModInt& rhs) {
        return lhs._v != rhs._v;
    }
    friend ModInt operator+(long long lhs, const ModInt& rhs) {
        return (ModInt(lhs) += rhs);
    }
    friend ModInt operator-(long long lhs, const ModInt& rhs) {
        return (ModInt(lhs) -= rhs);
    }
    friend ModInt operator*(long long lhs, const ModInt& rhs) {
        return (ModInt(lhs) *= rhs);
    }
    friend ostream& operator<<(ostream& os, const ModInt& M) {
        return os << M._v;
    }
    friend istream& operator>>(istream& is, ModInt& M) {
        long long x;
        is >> x;
        M = x;
        return is;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() {
        return m;
    }
};
#line 2 "library-cpp/mod/ModCombination.hpp"

#line 5 "library-cpp/mod/ModCombination.hpp"

template <class M> struct ModCombination {
  public:
    ModCombination() {
    }
    ModCombination(int n) : n_(n), fac_(n + 1), facinv_(n + 1) {
        assert(1 <= n);
        fac_[0] = 1;
        for (int i = 1; i <= n; i++) fac_[i] = fac_[i - 1] * i;
        facinv_[n] = M(1) / fac_[n];
        for (int i = n; i >= 1; i--) facinv_[i - 1] = facinv_[i] * i;
    }

    M fac(int k) const {
        assert(0 <= k and k <= n_);
        return fac_[k];
    }
    M facinv(int k) const {
        assert(0 <= k and k <= n_);
        return facinv_[k];
    }
    M inv(int k) const {
        assert(1 <= k and k <= n_);
        return facinv_[k] * fac_[k - 1];
    }

    M P(int n, int k) const {
        if (k < 0 or k > n) return M(0);
        assert(n <= n_);
        return fac_[n] * facinv_[n - k];
    }
    M C(int n, int k) const {
        if (k < 0 or k > n) return M(0);
        assert(n <= n_);
        return fac_[n] * facinv_[n - k] * facinv_[k];
    }

    /**
     * @note H(n, k) = (n 個 のボールを k 個の箱に分ける方法の数)
     * @note H(n, k) = C(n + k - 1, n)
     */
    M H(int n, int k) const {
        if (n == 0 and k == 0) return M(1);
        return C(n + k - 1, n);
    }
    M catalan(int n) const {
        if (n == 0) return M(1);
        return C(2 * n, n) - C(2 * n, n - 1);
    }

  private:
    int n_;
    std::vector<M> fac_, facinv_;
};
#line 5 "E.cpp"
using mint = ModInt<998244353>;
// using mint = ModInt<1000000007>;

template <class T, int sz> struct SquareMatrix {
    using arr = array<T, sz>;
    using mat = array<arr, sz>;

    SquareMatrix() : SquareMatrix(sz) {
    }
    SquareMatrix(int n) : n_(n) {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                A[i][j] = 0;
            }
        }
    }

    int size() const {
        return n_;
    }

    const arr& operator[](int i) const {
        assert(0 <= i and i < n_);
        return A[i];
    }
    arr& operator[](int i) {
        assert(0 <= i and i < n_);
        return A[i];
    }

    static SquareMatrix add_identity(int n_) {
        return SquareMatrix(n_);
    }
    static SquareMatrix mul_identity(int n_) {
        SquareMatrix I(n_);
        for (int i = 0; i < n_; i++) I[i][i] = 1;
        return I;
    }

    T add(T a, T b) const {
        return a + b;
    }

    T mul(T a, T b) const {
        return a * b;
    }

    SquareMatrix& operator+=(const SquareMatrix& B) {
        assert(B.size() == n_);
        for (int i = 0; i < n_; i++) {
            for (int j = 0; j < n_; j++) {
                (*this)[i][j] = add((*this)[i][j], B[i][j]);
            }
        }
        return *this;
    }

    SquareMatrix& operator*=(const SquareMatrix& B) {
        assert(B.size() == n_);
        SquareMatrix C(n_);
        for (int i = 0; i < n_; i++) {
            for (int k = 0; k < n_; k++) {
                for (int j = 0; j < n_; j++) {
                    C[i][j] = add(C[i][j], mul((*this)[i][k], B[k][j]));
                }
            }
        }
        A.swap(C.A);
        return *this;
    }

    SquareMatrix& operator^=(long long k) {
        SquareMatrix B = SquareMatrix::mul_identity(n_);
        while (k > 0) {
            if (k & 1) B *= *this;
            *this *= *this;
            k >>= 1;
        }
        A.swap(B.A);
        return *this;
    }

    SquareMatrix pow(long long k) const {
        SquareMatrix ret = *this;
        ret ^= k;
        return ret;
    }

    SquareMatrix operator+(const SquareMatrix& B) const {
        return (SquareMatrix(*this) += B);
    }
    SquareMatrix operator*(const SquareMatrix& B) const {
        return (SquareMatrix(*this) *= B);
    }
    SquareMatrix operator^(long long k) const {
        return (SquareMatrix(*this) ^= k);
    }
    bool operator==(const SquareMatrix& B) const {
        return A == B.A;
    }
    bool operator!=(const SquareMatrix& B) const {
        return A != B.A;
    }

    friend ostream& operator<<(ostream& os, SquareMatrix& B) {
        for (int i = 0; i < B.size(); i++) {
            os << "[";
            for (int j = 0; j < B.size(); j++) {
                os << B[i][j] << (j == B.size() - 1 ? "]\n" : ",");
            }
        }
        return os;
    }

    T determinant() const {
        SquareMatrix B = *this;
        T ret = 1;
        for (int i = 0; i < n_; i++) {
            int idx = -1;
            for (int j = i; j < n_; j++) {
                if (B[j][i] != 0) idx = j;
            }
            if (idx == -1) return T(0);
            if (i != idx) {
                ret *= -1;
                swap(B[i], B[idx]);
            }
            ret *= B[i][i];
            T inv = T(1) / B[i][i];
            for (int j = 0; j < n_; j++) {
                B[i][j] *= inv;
            }
            for (int j = i + 1; j < n_; j++) {
                T a = B[j][i];
                if (a == 0) continue;
                for (int k = 0; k < n_; k++) {
                    B[j][k] -= B[i][k] * a;
                }
            }
        }
        return ret;
    }

  private:
    int n_;
    mat A;
};

using Mat = SquareMatrix<mint, 6>;
void solve() {
    INT(N, Q);
    STR(S);

    auto f = [](const Mat& a, const Mat& b) { return b * a; };

    Mat zero, one, e;
    rep(i, 6) {
        zero[i][i] = 1;
        one[i][i] = 1;
        e[i][i] = 1;
    }
    zero[4][5] = 1;
    one[4][5] = 1;
    zero[2][4] = 1;
    zero[2][5] = 1;
    one[3][4] = 1;
    one[3][5] = 1;
    zero[1][3] = 1;
    one[1][2] = 1;
    zero[0][1] = 1;
    zero[0][3] = 1;
    one[0][1] = 1;
    one[0][2] = 1;
    vec<Mat> init(N);
    rep(i, N) {
        if (S[i] == '0') {
            init[i] = zero;
        } else {
            init[i] = one;
        }
    }
    SegmentTree seg(f, e, init);
    rep(Q) {
        INT(T);
        if (T == 1) {
            INT(i);
            i--;
            if (S[i] == '0') {
                seg.set(i, one);
                S[i] = '1';
            } else {
                seg.set(i, zero);
                S[i] = '0';
            }
        } else {
            INT(l, r);
            l--;
            Mat res = seg.get(l, r);
            print(res[0][5]);
        }
    }
}

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
    cerr << fixed << setprecision(7);

    int T = 1;
    // cin >> T;
    for (int test_case = 1; test_case <= T; test_case++) {
        // debug(test_case);
        solve();
    }
}