// Begin include: "../../template/template.hpp"
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
// Begin include: "util.hpp"
namespace yamada {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using lld = long double;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
template <typename T>
using VVV = vector<vector<vector<T>>>;
template <typename T>
using VVVV = vector<vector<vector<vector<T>>>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
using vvvl = vector<vector<vector<long long>>>;
using vvvvl = vector<vector<vector<vector<long long>>>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxpq = priority_queue<T, vector<T>, less<T>>;

template <typename T, typename U>
struct P : pair<T, U> {
	template <typename... Args>
	P(Args... args) : pair<T, U>(args...) {}

	using pair<T, U>::first;
	using pair<T, U>::second;

	P &operator+=(const P &r) {
		first += r.first;
		second += r.second;
		return *this;
	}
	P &operator-=(const P &r) {
		first -= r.first;
		second -= r.second;
		return *this;
	}
	P &operator*=(const P &r) {
		first *= r.first;
		second *= r.second;
		return *this;
	}
	template <typename S>
		P &operator*=(const S &r) {
			first *= r, second *= r;
			return *this;
		}
	P operator+(const P &r) const { return P(*this) += r; }
	P operator-(const P &r) const { return P(*this) -= r; }
	P operator*(const P &r) const { return P(*this) *= r; }
	template <typename S>
		P operator*(const S &r) const {
			return P(*this) *= r;
		}
	P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
using vvp = VV<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T, typename U>
inline bool amin(T &x, U y) {
	return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
	return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
	return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
	return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
	return accumulate(begin(v), end(v), T(0));
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
	return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
	return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
	long long ret = 1, x = 10;
	for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
	return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
	return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
	vector<T> ret(v.size() + 1);
	if (rev) {
		for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
	} else {
		for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
	}
	return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
	vector<T> ret(v);
	sort(ret.begin(), ret.end());
	ret.erase(unique(ret.begin(), ret.end()), ret.end());
	return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
	vector<int> ord(N);
	iota(begin(ord), end(ord), 0);
	sort(begin(ord), end(ord), f);
	return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
	int max_val = *max_element(begin(v), end(v));
	vector<int> inv(max_val + 1, -1);
	for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
	return inv;
}

vector<int> mkiota(int n) {
	vector<int> ret(n);
	iota(begin(ret), end(ret), 0);
	return ret;
}

template <typename T>
T mkrev(const T &v) {
	T w{v};
	reverse(begin(w), end(w));
	return w;
}

template <typename T>
bool nxp(T &v) {
	return next_permutation(begin(v), end(v));
}

// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
	vector<vector<T>> ret;
	vector<T> v;
	auto dfs = [&](auto rc, int i) -> void {
		if (i == (int)a.size()) {
			ret.push_back(v);
			return;
		}
		for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
	};
	dfs(dfs, 0);
	return ret;
}

template <typename T, typename U>
vector<U> Digit(T a, const U &x, int siz = -1) {
	vector<U> ret;
	while (a > 0) {
		ret.emplace_back(a % x);
		a /= x;
	}
	if (siz >= 0) while (ret.size() < siz) ret.emplace_back(0);
	return ret;
}

// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
	T res = I;
	for (; n; f(a = a * a), n >>= 1) {
		if (n & 1) f(res = res * a);
	}
	return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
	return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}

template <typename T>
T Rev(const T &v) {
	T res = v;
	reverse(begin(res), end(res));
	return res;
}

template <typename T>
vector<T> Transpose(const vector<T> &v) {
	using U = typename T::value_type;
	if(v.empty()) return {};
	int H = v.size(), W = v[0].size();
	vector res(W, T(H, U{}));
	for (int i = 0; i < H; i++) {
		for (int j = 0; j < W; j++) {
			res[j][i] = v[i][j];
		}
	}
	return res;
}

template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
	using U = typename T::value_type;
	int H = v.size(), W = v[0].size();
	vector res(W, T(H, U{}));
	for (int i = 0; i < H; i++) {
		for (int j = 0; j < W; j++) {
			if (clockwise) {
				res[W - 1 - j][i] = v[i][j];
			} else {
				res[j][H - 1 - i] = v[i][j];
			}
		}
	}
	return res;
}

template <typename T, typename F>
T bisect(T ok, T bad, F pred) {
	if (ok == bad) return ok;
	if (!pred(ok)) return ok; 
	while (bad - ok > 1) { T mid = ok + (bad - ok) / 2; (pred(mid) ? ok : bad) = mid; } 
	return bad;
}

template <typename T, typename F>
T bisect_double(T ok, T bad, F pred, int iter = 100) {
	if (ok == bad) return ok;
	if (!pred(ok)) return ok; 
	for (int i = 0; i < iter; i++){
		T mid = ok + (bad - ok) / 2; (pred(mid) ? ok : bad) = mid;
	} 
	return bad;
}

template <typename T>
bool inLR(T L, T x, T R){ return (L <= x && x < R); }

bool YESNO(bool b) { cout << (b ? "YES\n" : "NO\n"); return b; }
bool YesNo(bool b) { cout << (b ? "Yes\n" : "No\n"); return b; }

template <typename mint>
void mout(mint a, int M = 100) {
	if (a == 0) { cout << 0 << "\n"; return; }
	for (int i = 0; i <= M; i++) for (int j = 1; j <= M; j++) {
		mint val = (mint)i / j;
		if (val == a) {
			if (j == 1) cout << i << "\n";
			else cout << i << "/" << j << "\n";
			return;
		}
		else if (val == -a) {
			if (j == 1) cout << -i << "\n";
			else cout << -i << "/" << j << "\n";
			return;
		}
	}
	cout << "NF\n";
}

template <typename mint>
void mout(std::vector<mint> A, int M = 100) {
	int N = A.size();
	for (int pos = 0; pos < N; pos++) {
		if (A[pos] == 0) { cout << 0 << (pos == N - 1 ? "\n" : " "); continue; }

		bool fn = false;
		for (int i = 0; i <= M; i++) {
			for (int j = 1; j <= M; j++) {
				mint val = (mint)i / j;
				if (val == A[pos]) {
					if (j == 1) cout << i << (pos == N - 1 ? "\n" : " ");
					else cout << i << "/" << j << (pos == N - 1 ? "\n" : " ");
					fn = true;
					break;
				}
				else if (val == -A[pos]) {
					if (j == 1) cout << -i << (pos == N - 1 ? "\n" : " ");
					else cout << -i << "/" << j << (pos == N - 1 ? "\n" : " ");
					fn = true;
					break;
				}
			}
			if (fn) break;
		}
		if (!fn) cout << "NF" << (pos == N - 1 ? "\n" : " ");
	}
}

bool is_square(uint64_t n) {
	if (n < 2) return true;
	uint64_t r = static_cast<uint64_t>(sqrtl(static_cast<long double>(n)));
	if (r * r == n) return true;
	++r;
	return r * r == n;
}

template <typename T>
struct CumulativeSum {
	vector<T> S;
	CumulativeSum(vector<T> &A) {
		int N = A.size();
		S.resize(N + 1);
		for (int i = 0; i < N; i++) S[i + 1] = S[i] + A[i];
	}

	T query(int l, int r) { return (l <= r ? S[r] - S[l] : (T)0); }
	T get_val(int i) { return S[i + 1] - S[i]; }
};

} // namespace yamada

// End include: "util.hpp"

// bit operation
// Begin include: "bitop.hpp"
namespace yamada {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace yamada
// End include: "bitop.hpp"

// inout
// Begin include: "inout.hpp"
namespace yamada {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
	os << p.first << " " << p.second;
	return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
	is >> p.first >> p.second;
	return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
	int s = (int)v.size();
	for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
	return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
	for (auto &x : v) is >> x;
	return is;
}

istream &operator>>(istream &is, __int128_t &x) {
	string S;
	is >> S;
	x = 0;
	int flag = 0;
	for (auto &c : S) {
		if (c == '-') {
			flag = true;
			continue;
		}
		x *= 10;
		x += c - '0';
	}
	if (flag) x = -x;
	return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
	string S;
	is >> S;
	x = 0;
	for (auto &c : S) {
		x *= 10;
		x += c - '0';
	}
	return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
	if (x == 0) return os << 0;
	if (x < 0) os << '-', x = -x;
	string S;
	while (x) S.push_back('0' + x % 10), x /= 10;
	reverse(begin(S), end(S));
	return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
	if (x == 0) return os << 0;
	string S;
	while (x) S.push_back('0' + x % 10), x /= 10;
	reverse(begin(S), end(S));
	return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
	cin >> t;
	in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
	cout << t;
	if (sizeof...(u)) cout << sep;
	out(u...);
}

struct IoSetupYamada {
	IoSetupYamada() {
		cin.tie(nullptr);
		ios::sync_with_stdio(false);
		cout << fixed << setprecision(15);
		cerr << fixed << setprecision(7);
	}
} iosetupyamada;

}  // namespace yamada
// End include: "inout.hpp"

// macro
// Begin include: "macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define each3(x, y, z, v) for (auto&& [x, y, z] : v)
#define all(v) (v).begin(), (v).end()

#define rep1(a) for (long long _ = 0; _ < (long long)(a); ++_)
#define rep2(i, a) for (long long i = 0; i < (long long)(a); ++i)
#define rep3(i, a, b) for (long long i = a; i < (long long)(b); ++i)
#define rep4(i, a, b, c) for (long long i = a; i < (long long)(b); i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define rep1r(a) for (long long i = (long long)(a)-1; i >= 0LL; --i)
#define rep2r(i, a) for (long long i = (long long)(a)-1; i >= 0LL; --i)
#define rep3r(i, a, b) for (long long i = (long long)(b)-1; i >= (long long)(a); --i)
#define overload3(a, b, c, d, ...) d
#define repr(...) overload3(__VA_ARGS__, rep3r, rep2r, rep1r)(__VA_ARGS__)

#define eb emplace_back
#define mkp make_pair
#define mkt make_tuple
#define fi first
#define se second

#define vv(type, name, h, ...)  \
	vector<vector<type> > name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
	vector<vector<vector<type>>> name( \
			h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)  \
	vector<vector<vector<vector<type>>>> name( \
			a, vector<vector<vector<type>>>( \
				b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

#define ini(...)   \
	int __VA_ARGS__; \
	in(__VA_ARGS__)
#define inl(...)         \
	long long __VA_ARGS__; \
	in(__VA_ARGS__)
#define ins(...)      \
	string __VA_ARGS__; \
	in(__VA_ARGS__)
#define in2(s, t)                           \
	for (int i = 0; i < (int)s.size(); i++) { \
		in(s[i], t[i]);                         \
	}
#define in3(s, t, u)                        \
	for (int i = 0; i < (int)s.size(); i++) { \
		in(s[i], t[i], u[i]);                   \
	}
#define in4(s, t, u, v)                     \
	for (int i = 0; i < (int)s.size(); i++) { \
		in(s[i], t[i], u[i], v[i]);             \
	}
#define die(...)             \
	do {                       \
		yamada::out(__VA_ARGS__);\
		return;                  \
	} while (0)
// End include: "macro.hpp"

namespace yamada {
void solve();
}
int main() { yamada::solve(); }
// End include: "../../template/template.hpp"
// Begin include: "../../segment-tree/segment-tree.hpp"

template <typename T, typename F>
struct SegmentTree {
  int N;
  int size;
  vector<T> seg;
  const F f;
  const T I;

  SegmentTree(F _f, const T &I_) : N(0), size(0), f(_f), I(I_) {}

  SegmentTree(int _N, F _f, const T &I_) : f(_f), I(I_) { init(_N); }

  SegmentTree(const vector<T> &v, F _f, T I_) : f(_f), I(I_) {
    init(v.size());
    for (int i = 0; i < (int)v.size(); i++) {
      seg[i + size] = v[i];
    }
    build();
  }

  void init(int _N) {
    N = _N;
    size = 1;
    while (size < N) size <<= 1;
    seg.assign(2 * size, I);
  }

  void set(int k, T x) { seg[k + size] = x; }

  void build() {
    for (int k = size - 1; k > 0; k--) {
      seg[k] = f(seg[2 * k], seg[2 * k + 1]);
    }
  }

  void update(int k, T x) {
    k += size;
    seg[k] = x;
    while (k >>= 1) {
      seg[k] = f(seg[2 * k], seg[2 * k + 1]);
    }
  }

  void add(int k, T x) {
    k += size;
    seg[k] += x;
    while (k >>= 1) {
      seg[k] = f(seg[2 * k], seg[2 * k + 1]);
    }
  }

  // query to [a, b)
  T query(int a, int b) {
    T L = I, R = I;
    for (a += size, b += size; a < b; a >>= 1, b >>= 1) {
      if (a & 1) L = f(L, seg[a++]);
      if (b & 1) R = f(seg[--b], R);
    }
    return f(L, R);
  }

  T &operator[](const int &k) { return seg[k + size]; }

  // check(a[l] * ...  * a[r-1]) が true となる最大の r
  // (右端まですべて true なら N を返す)
  template <class C>
  int max_right(int l, C check) {
    assert(0 <= l && l <= N);
    assert(check(I) == true);
    if (l == N) return N;
    l += size;
    T sm = I;
    do {
      while (l % 2 == 0) l >>= 1;
      if (!check(f(sm, seg[l]))) {
        while (l < size) {
          l = (2 * l);
          if (check(f(sm, seg[l]))) {
            sm = f(sm, seg[l]);
            l++;
          }
        }
        return l - size;
      }
      sm = f(sm, seg[l]);
      l++;
    } while ((l & -l) != l);
    return N;
  }

  // check(a[l] * ... * a[r-1]) が true となる最小の l
  // (左端まで true なら 0 を返す)
  template <typename C>
  int min_left(int r, C check) {
    assert(0 <= r && r <= N);
    assert(check(I) == true);
    if (r == 0) return 0;
    r += size;
    T sm = I;
    do {
      r--;
      while (r > 1 && (r % 2)) r >>= 1;
      if (!check(f(seg[r], sm))) {
        while (r < size) {
          r = (2 * r + 1);
          if (check(f(seg[r], sm))) {
            sm = f(seg[r], sm);
            r--;
          }
        }
        return r + 1 - size;
      }
      sm = f(seg[r], sm);
    } while ((r & -r) != r);
    return 0;
  }
};
// End include: "../../segment-tree/segment-tree.hpp"
// Begin include: "../../matrix/matrix-fast.hpp"

template <typename T, int H, int W>
struct Matrix {
  using Array = array<array<T, W>, H>;
  Array A;

  Matrix() : A() {
    for (int i = 0; i < H; i++)
      for (int j = 0; j < W; j++) (*this)[i][j] = T();
  }

  int height() const { return H; }

  int width() const { return W; }

  inline const array<T, W> &operator[](int k) const { return A[k]; }

  inline array<T, W> &operator[](int k) { return A[k]; }

  static Matrix I() {
    assert(H == W);
    Matrix mat;
    for (int i = 0; i < H; i++) mat[i][i] = 1;
    return (mat);
  }

  Matrix &operator+=(const Matrix &B) {
    for (int i = 0; i < H; i++)
      for (int j = 0; j < W; j++) A[i][j] += B[i][j];
    return (*this);
  }

  Matrix &operator-=(const Matrix &B) {
    for (int i = 0; i < H; i++)
      for (int j = 0; j < W; j++) A[i][j] -= B[i][j];
    return (*this);
  }

  Matrix &operator*=(const Matrix &B) {
    assert(H == W);
    Matrix C;
    for (int i = 0; i < H; i++)
      for (int k = 0; k < H; k++)
        for (int j = 0; j < H; j++) C[i][j] += A[i][k] * B[k][j];
    A.swap(C.A);
    return (*this);
  }

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

  Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }

  Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }

  Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }

  Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }

  bool operator==(const Matrix &B) const {
    for (int i = 0; i < H; i++)
      for (int j = 0; j < W; j++)
        if (A[i][j] != B[i][j]) return false;
    return true;
  }

  bool operator!=(const Matrix &B) const {
    for (int i = 0; i < H; i++)
      for (int j = 0; j < W; j++)
        if (A[i][j] != B[i][j]) return true;
    return false;
  }

  friend ostream &operator<<(ostream &os,const Matrix &p) {
    for (int i = 0; i < H; i++) {
      os << "[";
      for (int j = 0; j < W; j++) {
        os << p[i][j] << (j + 1 == W ? "]\n" : ",");
      }
    }
    return (os);
  }

  T determinant(int n = -1) {
    if (n == -1) n = H;
    Matrix 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;
          break;
        }
      }
      if (idx == -1) return 0;
      if (i != idx) {
        ret *= T(-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 = i; k < n; k++) {
          B[j][k] -= B[i][k] * a;
        }
      }
    }
    return (ret);
  }
};

/**
 * @brief 行列ライブラリ(std::array版)
 */
// End include: "../../matrix/matrix-fast.hpp"
// Begin include: "../../modint/arbitrary-modint.hpp"

// Begin include: "barrett-reduction.hpp"

#include <utility>
using namespace std;

struct Barrett {
  using u32 = unsigned int;
  using i64 = long long;
  using u64 = unsigned long long;
  u32 m;
  u64 im;
  Barrett() : m(), im() {}
  Barrett(int n) : m(n), im(u64(-1) / m + 1) {}
  constexpr inline i64 quo(u64 n) {
    u64 x = u64((__uint128_t(n) * im) >> 64);
    u32 r = n - x * m;
    return m <= r ? x - 1 : x;
  }
  constexpr inline i64 rem(u64 n) {
    u64 x = u64((__uint128_t(n) * im) >> 64);
    u32 r = n - x * m;
    return m <= r ? r + m : r;
  }
  constexpr inline pair<i64, int> quorem(u64 n) {
    u64 x = u64((__uint128_t(n) * im) >> 64);
    u32 r = n - x * m;
    if (m <= r) return {x - 1, r + m};
    return {x, r};
  }
  constexpr inline i64 pow(u64 n, i64 p) {
    u32 a = rem(n), r = m == 1 ? 0 : 1;
    while (p) {
      if (p & 1) r = rem(u64(r) * a);
      a = rem(u64(a) * a);
      p >>= 1;
    }
    return r;
  }
};
// End include: "barrett-reduction.hpp"

template <int id>
struct ArbitraryModIntBase {
  int x;

  ArbitraryModIntBase() : x(0) {}

  ArbitraryModIntBase(int64_t y) {
    int z = y % get_mod();
    if (z < 0) z += get_mod();
    x = z;
  }

  ArbitraryModIntBase &operator+=(const ArbitraryModIntBase &p) {
    if ((x += p.x) >= get_mod()) x -= get_mod();
    return *this;
  }

  ArbitraryModIntBase &operator-=(const ArbitraryModIntBase &p) {
    if ((x += get_mod() - p.x) >= get_mod()) x -= get_mod();
    return *this;
  }

  ArbitraryModIntBase &operator*=(const ArbitraryModIntBase &p) {
    x = rem((unsigned long long)x * p.x);
    return *this;
  }

  ArbitraryModIntBase &operator/=(const ArbitraryModIntBase &p) {
    *this *= p.inverse();
    return *this;
  }

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

  ArbitraryModIntBase operator+(const ArbitraryModIntBase &p) const {
    return ArbitraryModIntBase(*this) += p;
  }

  ArbitraryModIntBase operator-(const ArbitraryModIntBase &p) const {
    return ArbitraryModIntBase(*this) -= p;
  }

  ArbitraryModIntBase operator*(const ArbitraryModIntBase &p) const {
    return ArbitraryModIntBase(*this) *= p;
  }

  ArbitraryModIntBase operator/(const ArbitraryModIntBase &p) const {
    return ArbitraryModIntBase(*this) /= p;
  }

  bool operator==(const ArbitraryModIntBase &p) const { return x == p.x; }

  bool operator!=(const ArbitraryModIntBase &p) const { return x != p.x; }

  ArbitraryModIntBase inverse() const {
    int a = x, b = get_mod(), u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ArbitraryModIntBase(u);
  }

  ArbitraryModIntBase pow(int64_t n) const {
    ArbitraryModIntBase ret(1), mul(x);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ArbitraryModIntBase &p) {
    return os << p.x;
  }

  friend istream &operator>>(istream &is, ArbitraryModIntBase &a) {
    int64_t t;
    is >> t;
    a = ArbitraryModIntBase(t);
    return (is);
  }

  int get() const { return x; }

  inline unsigned int rem(unsigned long long p) { return barrett().rem(p); }

  static inline Barrett &barrett() {
    static Barrett b;
    return b;
  }

  static inline int &get_mod() {
    static int mod = 0;
    return mod;
  }

  static void set_mod(int md) {
    assert(0 < md && md <= (1LL << 30) - 1);
    get_mod() = md;
    barrett() = Barrett(md);
  }
};

using ArbitraryModInt = ArbitraryModIntBase<-1>;

/**
 * @brief modint (2^{30} 未満の任意 mod 用)
 */
// End include: "../../modint/arbitrary-modint.hpp"

using mint=ArbitraryModInt;
void yamada::solve()
{
	inl(K,N);
	mint::set_mod(K);
	using T=Matrix<mint,2,2>;
	auto F=[&](T a,T b){return a*b;};
	T ti=T::I();

	V<T> init(N);
	rep(i,N){
		T a;
		rep(i,2)rep(j,2)in(a[i][j]);
		init[i]=a;
	}

	inl(Q);
	SegmentTree seg(init,F,ti);
	while(Q--){
		inl(pos,L,R); --L; --pos;
		T a; rep(i,2)rep(j,2)in(a[i][j]);
		seg.update(pos,a);
		a=seg.query(L,R);
		rep(i,2)out(a[i][0],a[i][1]);
	}
}