#if defined(local)
#include "/Users/noya/libra/my_template_compiled.hpp"
#else
#pragma GCC optimize("Ofast,unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define debug(...) 42
#define rep1(a) for (int i = 0; i < a; i++)
#define rep2(i, a) for (int i = 0; i < a; i++)
#define rep3(i, a, b) for (int i = a; i < b; i++)
#define rep4(i, a, b, c) for (int i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define pb emplace_back
template <typename T, typename T2> void cmin(T &x, const T2 &y) {
  x = x < y ? x : y;
}
template <typename T, typename T2> void cmax(T &x, const T2 &y) {
  x = x > y ? x : y;
}
using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
const int INF = 1000000000;
const ll LNF = 1000000000000000000;
#define sz(x) int((x).size())
#define all(x) begin(x), end(x)
#define fi first
#define se second
#endif



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


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

#if __cplusplus >= 202002L
#include <bit>
#endif

namespace atcoder {

namespace internal {

#if __cplusplus >= 202002L

using std::bit_ceil;

#else

// @return same with std::bit::bit_ceil
unsigned int bit_ceil(unsigned int n) {
  unsigned int x = 1;
  while (x < (unsigned int)(n))
    x *= 2;
  return x;
}

#endif

// @param n `1 <= n`
// @return same with std::bit::countr_zero
int countr_zero(unsigned int n) {
#ifdef _MSC_VER
  unsigned long index;
  _BitScanForward(&index, n);
  return index;
#else
  return __builtin_ctz(n);
#endif
}

// @param n `1 <= n`
// @return same with std::bit::countr_zero
constexpr int countr_zero_constexpr(unsigned int n) {
  int x = 0;
  while (!(n & (1 << x)))
    x++;
  return x;
}

} // namespace internal

} // namespace atcoder


namespace atcoder {

#if __cplusplus >= 201703L

template <class S, auto op, auto e, class F, auto mapping, auto composition,
          auto id>
struct lazy_segtree {
  static_assert(std::is_convertible_v<decltype(op), std::function<S(S, S)>>,
                "op must work as S(S, S)");
  static_assert(std::is_convertible_v<decltype(e), std::function<S()>>,
                "e must work as S()");
  static_assert(
      std::is_convertible_v<decltype(mapping), std::function<S(F, S)>>,
      "mapping must work as S(F, S)");
  static_assert(
      std::is_convertible_v<decltype(composition), std::function<F(F, F)>>,
      "composition must work as F(F, F)");
  static_assert(std::is_convertible_v<decltype(id), std::function<F()>>,
                "id must work as F()");

#else

template <class S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S),
          F (*composition)(F, F), F (*id)()>
struct lazy_segtree {

#endif

public:
  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())) {
    size = (int)internal::bit_ceil((unsigned int)(_n));
    log = internal::countr_zero((unsigned int)size);
    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);
  }

  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;
  }

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


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

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


#include <utility>

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

namespace atcoder {

namespace internal {

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

// @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


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

namespace atcoder {

namespace internal {

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

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

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

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

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

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

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

#else

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

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

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

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

#endif

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

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

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

} // namespace internal

} // namespace atcoder


namespace atcoder {

namespace internal {

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

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

} // namespace internal

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

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

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

  unsigned int val() const { return _v; }

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

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

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

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

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

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

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

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

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

  unsigned int val() const { return _v; }

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

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

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

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

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

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

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

namespace internal {

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

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

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

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

} // namespace internal

} // namespace atcoder


using mint = atcoder::modint1000000007;

using matrix = array<array<mint, 2>, 2>;

mt19937 rng(time(0));

matrix gen() {
  matrix a{};
  rep(i, 2) rep(j, 2) a[i][j] = rng();
  return a;
}

matrix inv(matrix a) {
  mint det = a[0][0] * a[1][1] - a[0][1] * a[1][0];
  assert(det.val() > 0);

  swap(a[0][0], a[1][1]);

  a[0][1] = -a[0][1];
  a[1][0] = -a[1][0];

  rep(i, 2) rep(j, 2) a[i][j] /= det;
  return a;
}

matrix operator*(const matrix &a, const matrix &b) {
  matrix c{};
  rep(i, 2) rep(j, 2) rep(k, 2) c[i][j] += a[i][k] * b[k][j];
  return c;
}

using type = array<matrix, 3>;
type op(type a, type b) {
  type c;
  rep(i, 3) c[i] = a[i] * b[i];
  return c;
}

matrix matrix_e() {
  matrix a{};
  a[0][0] = a[1][1] = 1;
  return a;
}

type e() {
  type a;
  rep(i, 3) a[i] = matrix_e();
  return a;
}

type mapping(int a, type b) {
  if (!a) {
    return b;
  }
  type c;
  for (int i = 0; i < 3; i++) {
    c[i] = b[(i + a) % 3];
  }
  return c;
}

int composition(int a, int b) { return (a + b) % 3; }

int id() { return 0; }

int main() {
  ios::sync_with_stdio(false);

  cin.tie(nullptr);

  int N, Q;
  cin >> N >> Q;

  string S;
  cin >> S;
  vector<int> A(N);

  for (int i = 0; i < N; i++) {
    A[i] = S[i] - '0';
  }
  type info;
  type info_inv;
  for (int i = 0; i < 3; i++) {
    info[i] = gen();
    info_inv[i] = inv(info[i]);

    assert(info[i] * info_inv[i] == matrix_e());
  }
  vector<type> a(N);
  for (int i = 0; i < N; i++) {
    if (i % 2 == 0)
      a[i] = mapping(A[i], info);
    else
      a[i] = mapping(A[i], info_inv);
  }
  atcoder::lazy_segtree<type, op, e, int, mapping, composition, id> seg(a);

  for (int i = 0; i < Q; i++) {
    int op, l, r;
    cin >> op >> l >> r;
    --l;
    if (op == 1) {
      seg.apply(l, r, {1});
    } else {
      auto cur = seg.prod(l, r);
      if (cur[0] == matrix_e()) {
        cout << "Yes\n";
      } else {
        cout << "No\n";
      }
    }
  }
  return 0;
}