#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#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__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sm = 0;
  for (auto &&a: A) sm += a;
  return sm;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}

template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
  vc<T> &res = first;
  (res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
#define FASTIO
#include <unistd.h>

// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
  char num[10000][4];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i][j] = n % 10 | '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

inline void load() {
  memcpy(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
  pil = 0;
  if (pir < SZ) ibuf[pir++] = '\n';
}

inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}

void rd(char &c) {
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
}

void rd(string &x) {
  x.clear();
  char c;
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
  do {
    x += c;
    if (pil == pir) load();
    c = ibuf[pil++];
  } while (!isspace(c));
}

template <typename T>
void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

template <typename T>
void rd_integer(T &x) {
  if (pil + 100 > pir) load();
  char c;
  do
    c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (c == '-') { minus = 1, c = ibuf[pil++]; }
  }
  x = 0;
  while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (minus) x = -x;
  }
}

void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }

template <class T, class U>
void rd(pair<T, U> &p) {
  return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
  if constexpr (N < std::tuple_size<T>::value) {
    auto &x = std::get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <class... T>
void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}

template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
  for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
  for (auto &d: x) rd(d);
}

void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
  rd(h), read(t...);
}

void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const string s) {
  for (char c: s) wt(c);
}
void wt(const char *s) {
  size_t len = strlen(s);
  for (size_t i = 0; i < len; i++) wt(s[i]);
}

template <typename T>
void wt_integer(T x) {
  if (por > SZ - 100) flush();
  if (x < 0) { obuf[por++] = '-', x = -x; }
  int outi;
  for (outi = 96; x >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[x % 10000], 4);
    x /= 10000;
  }
  if (x >= 1000) {
    memcpy(obuf + por, pre.num[x], 4);
    por += 4;
  } else if (x >= 100) {
    memcpy(obuf + por, pre.num[x] + 1, 3);
    por += 3;
  } else if (x >= 10) {
    int q = (x * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (x - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = x | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <typename T>
void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(15) << double(x);
  string s = oss.str();
  wt(s);
}

void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }

template <class T, class U>
void wt(const pair<T, U> val) {
  wt(val.first);
  wt(' ');
  wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
  if constexpr (N < std::tuple_size<T>::value) {
    if constexpr (N > 0) { wt(' '); }
    const auto x = std::get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(tuple<T...> tpl) {
  wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
template <class T>
void wt(const vector<T> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}

void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  wt(head);
  if (sizeof...(Tail)) wt(' ');
  print(forward<Tail>(tail)...);
}

// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;

#if defined(LOCAL)
#define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush()
#define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush()
#else
#define SHOW(...)
#endif

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define U32(...)   \
  u32 __VA_ARGS__; \
  read(__VA_ARGS__)
#define U64(...)   \
  u64 __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 3 "main.cpp"

#line 2 "/home/maspy/compro/library/ds/splaytree/splaytree.hpp"

/*
update でちゃんと prod が計算されてくれれば prod は op(lprod,x,rprod) でなくてもよい.
*/

// Node 型を別に定義して使う
template <typename Node>
struct SplayTree {
  Node *pool;
  const int NODES;
  int pid;
  using np = Node *;
  using X = typename Node::value_type;
  using A = typename Node::operator_type;
  vc<np> FREE;

  SplayTree(int NODES) : NODES(NODES), pid(0) { pool = new Node[NODES]; }
  ~SplayTree() { delete[] pool; }

  void free_subtree(np c) {
    if (!c) return;
    auto dfs = [&](auto &dfs, np c) -> void {
      if (c->l) dfs(dfs, c->l);
      if (c->r) dfs(dfs, c->r);
      FREE.eb(c);
    };
    dfs(dfs, c);
  }

  void reset() {
    pid = 0;
    FREE.clear();
  }

  np new_root() { return nullptr; }

  np new_node(const X &x) {
    assert(!FREE.empty() || pid < NODES);
    np n = (FREE.empty() ? &(pool[pid++]) : POP(FREE));
    Node::new_node(n, x);
    return n;
  }

  np new_node(const vc<X> &dat) {
    auto dfs = [&](auto &dfs, int l, int r) -> np {
      if (l == r) return nullptr;
      if (r == l + 1) return new_node(dat[l]);
      int m = (l + r) / 2;
      np l_root = dfs(dfs, l, m);
      np r_root = dfs(dfs, m + 1, r);
      np root = new_node(dat[m]);
      root->l = l_root, root->r = r_root;
      if (l_root) l_root->p = root;
      if (r_root) r_root->p = root;
      root->update();
      return root;
    };
    return dfs(dfs, 0, len(dat));
  }

  u32 get_size(np root) { return (root ? root->size : 0); }

  np merge(np l_root, np r_root) {
    if (!l_root) return r_root;
    if (!r_root) return l_root;
    assert((!l_root->p) && (!r_root->p));
    splay_kth(r_root, 0); // splay したので prop 済
    r_root->l = l_root;
    l_root->p = r_root;
    r_root->update();
    return r_root;
  }
  np merge3(np a, np b, np c) { return merge(merge(a, b), c); }
  np merge4(np a, np b, np c, np d) { return merge(merge(merge(a, b), c), d); }

  pair<np, np> split(np root, u32 k) {
    assert(!root || !root->p);
    if (k == 0) return {nullptr, root};
    if (k == (root->size)) return {root, nullptr};
    splay_kth(root, k - 1);
    np right = root->r;
    root->r = nullptr, right->p = nullptr;
    root->update();
    return {root, right};
  }
  tuple<np, np, np> split3(np root, u32 l, u32 r) {
    np nm, nr;
    tie(root, nr) = split(root, r);
    tie(root, nm) = split(root, l);
    return {root, nm, nr};
  }
  tuple<np, np, np, np> split4(np root, u32 i, u32 j, u32 k) {
    np d;
    tie(root, d) = split(root, k);
    auto [a, b, c] = split3(root, i, j);
    return {a, b, c, d};
  }

  // 部分木が区間 [l,r) に対応するようなノードを作って返す
  // そのノードが root になるわけではないので、
  // このノードを参照した後にすぐに splay して根に持ち上げること
  void goto_between(np &root, u32 l, u32 r) {
    if (l == 0 && r == root->size) return;
    if (l == 0) {
      splay_kth(root, r);
      root = root->l;
      return;
    }
    if (r == root->size) {
      splay_kth(root, l - 1);
      root = root->r;
      return;
    }
    splay_kth(root, r);
    np rp = root;
    root = rp->l;
    root->p = nullptr;
    splay_kth(root, l - 1);
    root->p = rp;
    rp->l = root;
    rp->update();
    root = root->r;
  }

  vc<X> get_all(const np &root) {
    vc<X> res;
    auto dfs = [&](auto &dfs, np root) -> void {
      if (!root) return;
      root->prop();
      dfs(dfs, root->l);
      res.eb(root->get());
      dfs(dfs, root->r);
    };
    dfs(dfs, root);
    return res;
  }

  X get(np &root, u32 k) {
    assert(root == nullptr || !root->p);
    splay_kth(root, k);
    return root->get();
  }

  void set(np &root, u32 k, const X &x) {
    assert(root != nullptr && !root->p);
    splay_kth(root, k);
    root->set(x);
  }

  void multiply(np &root, u32 k, const X &x) {
    assert(root != nullptr && !root->p);
    splay_kth(root, k);
    root->multiply(x);
  }

  X prod(np &root, u32 l, u32 r) {
    assert(root == nullptr || !root->p);
    using Mono = typename Node::Monoid_X;
    if (l == r) return Mono::unit();
    assert(0 <= l && l < r && r <= root->size);
    goto_between(root, l, r);
    X res = root->prod;
    splay(root, true);
    return res;
  }

  X prod(np &root) {
    assert(root == nullptr || !root->p);
    using Mono = typename Node::Monoid_X;
    return (root ? root->prod : Mono::unit());
  }

  void apply(np &root, u32 l, u32 r, const A &a) {
    if (l == r) return;
    assert(0 <= l && l < r && r <= root->size);
    goto_between(root, l, r);
    root->apply(a);
    splay(root, true);
  }
  void apply(np &root, const A &a) {
    if (!root) return;
    root->apply(a);
  }

  void reverse(np &root, u32 l, u32 r) {
    assert(root == nullptr || !root->p);
    if (l == r) return;
    assert(0 <= l && l < r && r <= root->size);
    goto_between(root, l, r);
    root->reverse();
    splay(root, true);
  }
  void reverse(np root) {
    if (!root) return;
    root->reverse();
  }

  void rotate(Node *n) {
    // n を根に近づける。prop, update は rotate の外で行う。
    Node *pp, *p, *c;
    p = n->p;
    pp = p->p;
    if (p->l == n) {
      c = n->r;
      n->r = p;
      p->l = c;
    } else {
      c = n->l;
      n->l = p;
      p->r = c;
    }
    if (pp && pp->l == p) pp->l = n;
    if (pp && pp->r == p) pp->r = n;
    n->p = pp;
    p->p = n;
    if (c) c->p = p;
  }

  void prop_from_root(np c) {
    if (!c->p) {
      c->prop();
      return;
    }
    prop_from_root(c->p);
    c->prop();
  }

  void splay(Node *me, bool prop_from_root_done) {
    // これを呼ぶ時点で、me の祖先（me を除く）は既に prop 済であることを仮定
    // 特に、splay 終了時点で me は upd / prop 済である
    if (!prop_from_root_done) prop_from_root(me);
    me->prop();
    while (me->p) {
      np p = me->p;
      np pp = p->p;
      if (!pp) {
        rotate(me);
        p->update();
        break;
      }
      bool same = (p->l == me && pp->l == p) || (p->r == me && pp->r == p);
      if (same) rotate(p), rotate(me);
      if (!same) rotate(me), rotate(me);
      pp->update(), p->update();
    }
    // me の update は最後だけでよい
    me->update();
  }

  void splay_kth(np &root, u32 k) {
    assert(0 <= k && k < (root->size));
    while (1) {
      root->prop();
      u32 sl = (root->l ? root->l->size : 0);
      if (k == sl) break;
      if (k < sl)
        root = root->l;
      else {
        k -= sl + 1;
        root = root->r;
      }
    }
    splay(root, true);
  }

  // check(x), 左側のノード全体が check を満たすように切る
  template <typename F>
  pair<np, np> split_max_right(np root, F check) {
    if (!root) return {nullptr, nullptr};
    assert(!root->p);
    np c = find_max_right(root, check);
    if (!c) {
      splay(root, true);
      return {nullptr, root};
    }
    splay(c, true);
    np right = c->r;
    if (!right) return {c, nullptr};
    right->p = nullptr;
    c->r = nullptr;
    c->update();
    return {c, right};
  }

  // check(x, cnt), 左側のノード全体が check を満たすように切る
  template <typename F>
  pair<np, np> split_max_right_cnt(np root, F check) {
    if (!root) return {nullptr, nullptr};
    assert(!root->p);
    np c = find_max_right_cnt(root, check);
    if (!c) {
      splay(root, true);
      return {nullptr, root};
    }
    splay(c, true);
    np right = c->r;
    if (!right) return {c, nullptr};
    right->p = nullptr;
    c->r = nullptr;
    c->update();
    return {c, right};
  }

  // 左側のノード全体の prod が check を満たすように切る
  template <typename F>
  pair<np, np> split_max_right_prod(np root, F check) {
    if (!root) return {nullptr, nullptr};
    assert(!root->p);
    np c = find_max_right_prod(root, check);
    if (!c) {
      splay(root, true);
      return {nullptr, root};
    }
    splay(c, true);
    np right = c->r;
    if (!right) return {c, nullptr};
    right->p = nullptr;
    c->r = nullptr;
    c->update();
    return {c, right};
  }

  template <typename F>
  np find_max_right(np root, const F &check) {
    // 最後に見つけた ok の点、最後に探索した点
    np last_ok = nullptr, last = nullptr;
    while (root) {
      last = root;
      root->prop();
      if (check(root->x)) {
        last_ok = root;
        root = root->r;
      } else {
        root = root->l;
      }
    }
    splay(last, true);
    return last_ok;
  }

  template <typename F>
  np find_max_right_cnt(np root, const F &check) {
    // 最後に見つけた ok の点、最後に探索した点
    np last_ok = nullptr, last = nullptr;
    ll n = 0;
    while (root) {
      last = root;
      root->prop();
      ll ns = (root->l ? root->l->size : 0);
      if (check(root->x, n + ns + 1)) {
        last_ok = root;
        n += ns + 1;
        root = root->r;
      } else {
        root = root->l;
      }
    }
    splay(last, true);
    return last_ok;
  }

  template <typename F>
  np find_max_right_prod(np root, const F &check) {
    using Mono = typename Node::Monoid_X;
    X prod = Mono::unit();
    // 最後に見つけた ok の点、最後に探索した点
    np last_ok = nullptr, last = nullptr;
    while (root) {
      last = root;
      root->prop();
      np tmp = root->r;
      root->r = nullptr;
      root->update();
      X lprod = Mono::op(prod, root->prod);
      root->r = tmp;
      root->update();
      if (check(lprod)) {
        prod = lprod;
        last_ok = root;
        root = root->r;
      } else {
        root = root->l;
      }
    }
    splay(last, true);
    return last_ok;
  }
};
#line 2 "/home/maspy/compro/library/ds/splaytree/splaytree_basic.hpp"

namespace SplayTreeNodes {
template <typename S>
struct Node_Basic {
  using value_type = S;
  using operator_type = int;
  using np = Node_Basic *;

  np p, l, r;
  bool rev;
  S x;
  u32 size;

  static void new_node(np n, const S &x) {
    n->p = n->l = n->r = nullptr;
    n->x = x, n->size = 1, n->rev = 0;
  }

  void update() {
    size = 1;
    if (l) { size += l->size; }
    if (r) { size += r->size; }
  }

  void prop() {
    if (rev) {
      if (l) { l->rev ^= 1, swap(l->l, l->r); }
      if (r) { r->rev ^= 1, swap(r->l, r->r); }
      rev = 0;
    }
  }

  // update, prop 以外で呼ばれるものは、splay 後であることが想定されている。
  // したがってその時点で update, prop 済であることを仮定してよい。
  S get() { return x; }
  void set(const S &xx) {
    x = xx;
    update();
  }
  void reverse() {
    swap(l, r);
    rev ^= 1;
  }
};
template <typename S>
using SplayTree_Basic = SplayTree<Node_Basic<S>>;
} // namespace SplayTreeNodes

using SplayTreeNodes::SplayTree_Basic;
#line 5 "main.cpp"

/*
aX, |X|=k
Yb, |Y|=k-1

aYb
X

Xb
aY

2回でひとつもってこれる
多い方からスタートしておく
*/

struct Data {
  int N, K;
  int idx = 0;
  deque<int> L, R;
  Data(int N, int K, vc<int> A) : N(N), K(K) {
    FOR(i, K) L.eb(A[i]);
    FOR(i, K, N) R.eb(A[i]);
  }
  void rot() {
    ++idx;
    idx %= N;
    L.emplace_back(POP(R));
    R.emplace_back(POP(L));
  }
  void rev_rot() {
    idx += N - 1;
    idx %= N;
    L.push_front(R.back()), R.pop_back();
    R.push_front(L.back()), L.pop_back();
  }
  void debug() {
    vc<int> S(all(L));
    vc<int> T(all(R));
    SHOW(S, T);
  }
};

void solve() {
  LL(N, K);
  vc<int> X, Y;
  {
    STR(A, B);
    int b = count(all(A), 'B');
    int c = count(all(A), 'C');
    if (b > c) {
      for (auto& x: A) x = 'B' ^ 'C' ^ x;
      for (auto& x: B) x = 'B' ^ 'C' ^ x;
    }
    for (auto& x: A) X.eb(x == 'B');
    for (auto& x: B) Y.eb(x == 'B');
  }

  int n = SUM<int>(X);
  Data A(N, K, X), B(N, K, Y);
  vc<pi> ANS;

  FOR(n) {
    while (A.L[0] != 1) A.rot();
    while (B.L.back() != 0) B.rev_rot();
    // A.debug();
    // B.debug();
    ANS.eb(A.idx + 1, B.idx);
    ANS.eb(A.idx, B.idx);
    A.L.pop_front();
    A.L.push_back(POP(A.R));
    A.R.push_front(0);
    B.L.pop_back();
    B.L.push_front(1);
  }
  print(len(ANS));
  for (auto& [a, b]: ANS) print(1 + a % N, 1 + b % N);
}

signed main() { solve(); }