/**
 *  date : 2023-02-25 13:29:31
 */

#define NDEBUG
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
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = 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>>;

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>;

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

template <typename T>
int sz(const T &t) {
  return t.size();
}

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), 0LL);
}

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(vector<T> &v) {
  return next_permutation(begin(v), end(v));
}

template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

}  // namespace Nyaan

// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(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 Nyaan

// inout
namespace Nyaan {

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...);
}

void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
  cout << t;
  outr(u...);
}

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

}  // namespace Nyaan

// debug

#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif

#ifdef NyaanLocal
#define trc2(...) (void(0))
#else
#define trc2(...) (void(0))
#endif

// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#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 {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }

//
using namespace Nyaan;




namespace atcoder {

namespace internal {

std::vector<int> sa_naive(const std::vector<int>& s) {
    int n = int(s.size());
    std::vector<int> sa(n);
    std::iota(sa.begin(), sa.end(), 0);
    std::sort(sa.begin(), sa.end(), [&](int l, int r) {
        if (l == r) return false;
        while (l < n && r < n) {
            if (s[l] != s[r]) return s[l] < s[r];
            l++;
            r++;
        }
        return l == n;
    });
    return sa;
}

std::vector<int> sa_doubling(const std::vector<int>& s) {
    int n = int(s.size());
    std::vector<int> sa(n), rnk = s, tmp(n);
    std::iota(sa.begin(), sa.end(), 0);
    for (int k = 1; k < n; k *= 2) {
        auto cmp = [&](int x, int y) {
            if (rnk[x] != rnk[y]) return rnk[x] < rnk[y];
            int rx = x + k < n ? rnk[x + k] : -1;
            int ry = y + k < n ? rnk[y + k] : -1;
            return rx < ry;
        };
        std::sort(sa.begin(), sa.end(), cmp);
        tmp[sa[0]] = 0;
        for (int i = 1; i < n; i++) {
            tmp[sa[i]] = tmp[sa[i - 1]] + (cmp(sa[i - 1], sa[i]) ? 1 : 0);
        }
        std::swap(tmp, rnk);
    }
    return sa;
}

// SA-IS, linear-time suffix array construction
// Reference:
// G. Nong, S. Zhang, and W. H. Chan,
// Two Efficient Algorithms for Linear Time Suffix Array Construction
template <int THRESHOLD_NAIVE = 10, int THRESHOLD_DOUBLING = 40>
std::vector<int> sa_is(const std::vector<int>& s, int upper) {
    int n = int(s.size());
    if (n == 0) return {};
    if (n == 1) return {0};
    if (n == 2) {
        if (s[0] < s[1]) {
            return {0, 1};
        } else {
            return {1, 0};
        }
    }
    if (n < THRESHOLD_NAIVE) {
        return sa_naive(s);
    }
    if (n < THRESHOLD_DOUBLING) {
        return sa_doubling(s);
    }

    std::vector<int> sa(n);
    std::vector<bool> ls(n);
    for (int i = n - 2; i >= 0; i--) {
        ls[i] = (s[i] == s[i + 1]) ? ls[i + 1] : (s[i] < s[i + 1]);
    }
    std::vector<int> sum_l(upper + 1), sum_s(upper + 1);
    for (int i = 0; i < n; i++) {
        if (!ls[i]) {
            sum_s[s[i]]++;
        } else {
            sum_l[s[i] + 1]++;
        }
    }
    for (int i = 0; i <= upper; i++) {
        sum_s[i] += sum_l[i];
        if (i < upper) sum_l[i + 1] += sum_s[i];
    }

    auto induce = [&](const std::vector<int>& lms) {
        std::fill(sa.begin(), sa.end(), -1);
        std::vector<int> buf(upper + 1);
        std::copy(sum_s.begin(), sum_s.end(), buf.begin());
        for (auto d : lms) {
            if (d == n) continue;
            sa[buf[s[d]]++] = d;
        }
        std::copy(sum_l.begin(), sum_l.end(), buf.begin());
        sa[buf[s[n - 1]]++] = n - 1;
        for (int i = 0; i < n; i++) {
            int v = sa[i];
            if (v >= 1 && !ls[v - 1]) {
                sa[buf[s[v - 1]]++] = v - 1;
            }
        }
        std::copy(sum_l.begin(), sum_l.end(), buf.begin());
        for (int i = n - 1; i >= 0; i--) {
            int v = sa[i];
            if (v >= 1 && ls[v - 1]) {
                sa[--buf[s[v - 1] + 1]] = v - 1;
            }
        }
    };

    std::vector<int> lms_map(n + 1, -1);
    int m = 0;
    for (int i = 1; i < n; i++) {
        if (!ls[i - 1] && ls[i]) {
            lms_map[i] = m++;
        }
    }
    std::vector<int> lms;
    lms.reserve(m);
    for (int i = 1; i < n; i++) {
        if (!ls[i - 1] && ls[i]) {
            lms.push_back(i);
        }
    }

    induce(lms);

    if (m) {
        std::vector<int> sorted_lms;
        sorted_lms.reserve(m);
        for (int v : sa) {
            if (lms_map[v] != -1) sorted_lms.push_back(v);
        }
        std::vector<int> rec_s(m);
        int rec_upper = 0;
        rec_s[lms_map[sorted_lms[0]]] = 0;
        for (int i = 1; i < m; i++) {
            int l = sorted_lms[i - 1], r = sorted_lms[i];
            int end_l = (lms_map[l] + 1 < m) ? lms[lms_map[l] + 1] : n;
            int end_r = (lms_map[r] + 1 < m) ? lms[lms_map[r] + 1] : n;
            bool same = true;
            if (end_l - l != end_r - r) {
                same = false;
            } else {
                while (l < end_l) {
                    if (s[l] != s[r]) {
                        break;
                    }
                    l++;
                    r++;
                }
                if (l == n || s[l] != s[r]) same = false;
            }
            if (!same) rec_upper++;
            rec_s[lms_map[sorted_lms[i]]] = rec_upper;
        }

        auto rec_sa =
            sa_is<THRESHOLD_NAIVE, THRESHOLD_DOUBLING>(rec_s, rec_upper);

        for (int i = 0; i < m; i++) {
            sorted_lms[i] = lms[rec_sa[i]];
        }
        induce(sorted_lms);
    }
    return sa;
}

}  // namespace internal

std::vector<int> suffix_array(const std::vector<int>& s, int upper) {
    assert(0 <= upper);
    for (int d : s) {
        assert(0 <= d && d <= upper);
    }
    auto sa = internal::sa_is(s, upper);
    return sa;
}

template <class T> std::vector<int> suffix_array(const std::vector<T>& s) {
    int n = int(s.size());
    std::vector<int> idx(n);
    iota(idx.begin(), idx.end(), 0);
    sort(idx.begin(), idx.end(), [&](int l, int r) { return s[l] < s[r]; });
    std::vector<int> s2(n);
    int now = 0;
    for (int i = 0; i < n; i++) {
        if (i && s[idx[i - 1]] != s[idx[i]]) now++;
        s2[idx[i]] = now;
    }
    return internal::sa_is(s2, now);
}

std::vector<int> suffix_array(const std::string& s) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return internal::sa_is(s2, 255);
}

// Reference:
// T. Kasai, G. Lee, H. Arimura, S. Arikawa, and K. Park,
// Linear-Time Longest-Common-Prefix Computation in Suffix Arrays and Its
// Applications
template <class T>
std::vector<int> lcp_array(const std::vector<T>& s,
                           const std::vector<int>& sa) {
    int n = int(s.size());
    assert(n >= 1);
    std::vector<int> rnk(n);
    for (int i = 0; i < n; i++) {
        rnk[sa[i]] = i;
    }
    std::vector<int> lcp(n - 1);
    int h = 0;
    for (int i = 0; i < n; i++) {
        if (h > 0) h--;
        if (rnk[i] == 0) continue;
        int j = sa[rnk[i] - 1];
        for (; j + h < n && i + h < n; h++) {
            if (s[j + h] != s[i + h]) break;
        }
        lcp[rnk[i] - 1] = h;
    }
    return lcp;
}

std::vector<int> lcp_array(const std::string& s, const std::vector<int>& sa) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return lcp_array(s2, sa);
}

// Reference:
// D. Gusfield,
// Algorithms on Strings, Trees, and Sequences: Computer Science and
// Computational Biology
template <class T> std::vector<int> z_algorithm(const std::vector<T>& s) {
    int n = int(s.size());
    if (n == 0) return {};
    std::vector<int> z(n);
    z[0] = 0;
    for (int i = 1, j = 0; i < n; i++) {
        int& k = z[i];
        k = (j + z[j] <= i) ? 0 : std::min(j + z[j] - i, z[i - j]);
        while (i + k < n && s[k] == s[i + k]) k++;
        if (j + z[j] < i + z[i]) j = i;
    }
    z[0] = n;
    return z;
}

std::vector<int> z_algorithm(const std::string& s) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return z_algorithm(s2);
}

}  // namespace atcoder


using namespace std;

template <typename T>
struct SparseTable {
  inline static constexpr T INF = numeric_limits<T>::max() / 2;
  int N;
  vector<vector<T> > table;
  T f(T a, T b) { return min(a, b); }
  SparseTable() {}
  SparseTable(const vector<T> &v) : N(v.size()) {
    int b = 1;
    while ((1 << b) <= N) ++b;
    table.push_back(v);
    for (int i = 1; i < b; i++) {
      table.push_back(vector<T>(N, INF));
      for (int j = 0; j + (1 << i) <= N; j++) {
        table[i][j] = f(table[i - 1][j], table[i - 1][j + (1 << (i - 1))]);
      }
    }
  }
  // [l, r)
  T query(int l, int r) {
    assert(0 <= l and l <= r and r <= N);
    if (l == r) return INF;
    int b = 31 - __builtin_clz(r - l);
    return f(table[b][l], table[b][r - (1 << b)]);
  }
};

/**
 * @brief Sparse Table
 */

template <typename Container>
struct StringSearch {
  const Container& S;
  int N;
  vector<int> sa, la, invsa;
  SparseTable<int> sparse;

  StringSearch(const Container& _s) : S(_s), N(S.size()) {
    sa = atcoder::suffix_array(S);
    la = atcoder::lcp_array(S, sa);
    invsa.resize(N);
    for (int i = 0; i < N; i++) invsa[sa[i]] = i;
    sparse = SparseTable<int>{la};
  }

  // lcp(s[i, N), s[j, N))
  int lcp(int i, int j) {
    assert(0 <= min(i, j) and max(i, j) < N);
    if (i == j) return N - i;
    int x = min(invsa[i], invsa[j]);
    int y = max(invsa[i], invsa[j]);
    return sparse.query(x, y);
  }
  // lcp(s[a, b), s[c, d))
  int lcp(int a, int b, int c, int d) {
    assert(0 <= a and a <= b and b <= N);
    assert(0 <= c and c <= d and d <= N);
    int l = lcp(a, c);
    return min({l, b - a, d - c});
  }
  // lcp(s[a, b), s[c, d))
  template <typename Int>
  int lcp(pair<Int, Int> p, pair<Int, Int> q) {
    return lcp(p.first, p.second, q.first, q.second);
  }

  // s[i, N) > s[j, N) : 1
  // s[i, N) = s[j, N) : 0
  // s[i, N) < s[j, N) : -1
  int strcmp(int i, int j) {
    assert(0 <= min(i, j) and max(i, j) < N);
    if (i == j) return 0;
    return invsa[i] < invsa[j] ? -1 : 1;
  }

  // s[a, b) > s[c, d) : 1
  // s[a, b) = s[c, d) : 0
  // s[a, b) < s[c, d) : -1
  int strcmp(int a, int b, int c, int d) {
    int l = lcp(a, b, c, d);
    return a + l == b            ? (c + l == d ? 0 : -1)
           : c + l == d          ? 1
           : S[a + l] < S[c + l] ? -1
                                 : 1;
  }
  // s[a, b) > s[c, d) : 1
  // s[a, b) = s[c, d) : 0
  // s[a, b) < s[c, d) : -1
  template <typename Int>
  int strcmp(pair<Int, Int> p, pair<Int, Int> q) {
    return strcmp(p.first, p.second, q.first, q.second);
  }
};


using namespace std;




template <uint32_t mod>
struct LazyMontgomeryModInt {
  using mint = LazyMontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod;
    for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
    return ret;
  }

  static constexpr u32 r = get_r();
  static constexpr u32 n2 = -u64(mod) % mod;
  static_assert(r * mod == 1, "invalid, r * mod != 1");
  static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");

  u32 a;

  constexpr LazyMontgomeryModInt() : a(0) {}
  constexpr LazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};

  static constexpr u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
  }

  constexpr mint &operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }

  constexpr mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
  constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
  constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
  constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
  constexpr bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr mint operator-() const { return mint() - mint(*this); }

  constexpr mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  
  constexpr mint inverse() const { return pow(mod - 2); }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = LazyMontgomeryModInt<mod>(t);
    return (is);
  }
  
  constexpr u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static constexpr u32 get_mod() { return mod; }
};
template <typename mint>
struct NTT {
  static constexpr uint32_t get_pr() {
    uint32_t _mod = mint::get_mod();
    using u64 = uint64_t;
    u64 ds[32] = {};
    int idx = 0;
    u64 m = _mod - 1;
    for (u64 i = 2; i * i <= m; ++i) {
      if (m % i == 0) {
        ds[idx++] = i;
        while (m % i == 0) m /= i;
      }
    }
    if (m != 1) ds[idx++] = m;

    uint32_t _pr = 2;
    while (1) {
      int flg = 1;
      for (int i = 0; i < idx; ++i) {
        u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;
        while (b) {
          if (b & 1) r = r * a % _mod;
          a = a * a % _mod;
          b >>= 1;
        }
        if (r == 1) {
          flg = 0;
          break;
        }
      }
      if (flg == 1) break;
      ++_pr;
    }
    return _pr;
  };

  static constexpr uint32_t mod = mint::get_mod();
  static constexpr uint32_t pr = get_pr();
  static constexpr int level = __builtin_ctzll(mod - 1);
  mint dw[level], dy[level];

  void setwy(int k) {
    mint w[level], y[level];
    w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
    y[k - 1] = w[k - 1].inverse();
    for (int i = k - 2; i > 0; --i)
      w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
    dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
    for (int i = 3; i < k; ++i) {
      dw[i] = dw[i - 1] * y[i - 2] * w[i];
      dy[i] = dy[i - 1] * w[i - 2] * y[i];
    }
  }

  NTT() { setwy(level); }

  void fft4(vector<mint> &a, int k) {
    if ((int)a.size() <= 1) return;
    if (k == 1) {
      mint a1 = a[1];
      a[1] = a[0] - a[1];
      a[0] = a[0] + a1;
      return;
    }
    if (k & 1) {
      int v = 1 << (k - 1);
      for (int j = 0; j < v; ++j) {
        mint ajv = a[j + v];
        a[j + v] = a[j] - ajv;
        a[j] += ajv;
      }
    }
    int u = 1 << (2 + (k & 1));
    int v = 1 << (k - 2 - (k & 1));
    mint one = mint(1);
    mint imag = dw[1];
    while (v) {
      // jh = 0
      {
        int j0 = 0;
        int j1 = v;
        int j2 = j1 + v;
        int j3 = j2 + v;
        for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
          mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
          mint t0p2 = t0 + t2, t1p3 = t1 + t3;
          mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
          a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
          a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
        }
      }
      // jh >= 1
      mint ww = one, xx = one * dw[2], wx = one;
      for (int jh = 4; jh < u;) {
        ww = xx * xx, wx = ww * xx;
        int j0 = jh * v;
        int je = j0 + v;
        int j2 = je + v;
        for (; j0 < je; ++j0, ++j2) {
          mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
               t3 = a[j2 + v] * wx;
          mint t0p2 = t0 + t2, t1p3 = t1 + t3;
          mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
          a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
          a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
        }
        xx *= dw[__builtin_ctzll((jh += 4))];
      }
      u <<= 2;
      v >>= 2;
    }
  }

  void ifft4(vector<mint> &a, int k) {
    if ((int)a.size() <= 1) return;
    if (k == 1) {
      mint a1 = a[1];
      a[1] = a[0] - a[1];
      a[0] = a[0] + a1;
      return;
    }
    int u = 1 << (k - 2);
    int v = 1;
    mint one = mint(1);
    mint imag = dy[1];
    while (u) {
      // jh = 0
      {
        int j0 = 0;
        int j1 = v;
        int j2 = v + v;
        int j3 = j2 + v;
        for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
          mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
          mint t0p1 = t0 + t1, t2p3 = t2 + t3;
          mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
          a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
          a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
        }
      }
      // jh >= 1
      mint ww = one, xx = one * dy[2], yy = one;
      u <<= 2;
      for (int jh = 4; jh < u;) {
        ww = xx * xx, yy = xx * imag;
        int j0 = jh * v;
        int je = j0 + v;
        int j2 = je + v;
        for (; j0 < je; ++j0, ++j2) {
          mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
          mint t0p1 = t0 + t1, t2p3 = t2 + t3;
          mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
          a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
          a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;
        }
        xx *= dy[__builtin_ctzll(jh += 4)];
      }
      u >>= 4;
      v <<= 2;
    }
    if (k & 1) {
      u = 1 << (k - 1);
      for (int j = 0; j < u; ++j) {
        mint ajv = a[j] - a[j + u];
        a[j] += a[j + u];
        a[j + u] = ajv;
      }
    }
  }

  void ntt(vector<mint> &a) {
    if ((int)a.size() <= 1) return;
    fft4(a, __builtin_ctz(a.size()));
  }

  void intt(vector<mint> &a) {
    if ((int)a.size() <= 1) return;
    ifft4(a, __builtin_ctz(a.size()));
    mint iv = mint(a.size()).inverse();
    for (auto &x : a) x *= iv;
  }

  vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
    int l = a.size() + b.size() - 1;
    if (min<int>(a.size(), b.size()) <= 40) {
      vector<mint> s(l);
      for (int i = 0; i < (int)a.size(); ++i)
        for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];
      return s;
    }
    int k = 2, M = 4;
    while (M < l) M <<= 1, ++k;
    setwy(k);
    vector<mint> s(M), t(M);
    for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];
    for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];
    fft4(s, k);
    fft4(t, k);
    for (int i = 0; i < M; ++i) s[i] *= t[i];
    ifft4(s, k);
    s.resize(l);
    mint invm = mint(M).inverse();
    for (int i = 0; i < l; ++i) s[i] *= invm;
    return s;
  }

  void ntt_doubling(vector<mint> &a) {
    int M = (int)a.size();
    auto b = a;
    intt(b);
    mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
    for (int i = 0; i < M; i++) b[i] *= r, r *= zeta;
    ntt(b);
    copy(begin(b), end(b), back_inserter(a));
  }
};

namespace WildcardPatternMatchingImpl {

template <typename Container, unsigned int MOD>
vector<int> inner(const Container& a, const Container& b,
                  const typename Container::value_type& wildcard = 0) {
  using mint = LazyMontgomeryModInt<MOD>;
  static NTT<mint> ntt;
  int N = a.size(), M = b.size();
  vector<mint> A1(N), A2(N), A3(N), B1(M), B2(M), B3(M);
  for (int i = 0; i < N; i++) {
    mint x = a[i] == wildcard ? 0 : a[i];
    mint y = a[i] == wildcard ? 0 : 1;
    A1[i] = y * x * x;
    A2[i] = y * x * (-2);
    A3[i] = y;
  }
  for (int i = 0; i < M; i++) {
    mint x = b[i] == wildcard ? 0 : b[i];
    mint y = b[i] == wildcard ? 0 : 1;
    B1[M - 1 - i] = y;
    B2[M - 1 - i] = y * x;
    B3[M - 1 - i] = y * x * x;
  }
  auto AB1 = ntt.multiply(A1, B1);
  auto AB2 = ntt.multiply(A2, B2);
  auto AB3 = ntt.multiply(A3, B3);
  vector<int> res(N - M + 1, 1);
  for (int i = 0; i < N - M + 1; i++) {
    mint x = AB1[i + M - 1] + AB2[i + M - 1] + AB3[i + M - 1];
    trc(i, x);
    if (x != 0) res[i] = 0;
  }
  return res;
}

// 返り値 : 長さ |a| - |b| + 1 の配列 c
// c[i] := a[i, i+|b|) b とマッチするならば 1, しなければ 0)
// wildcard は引数に入れる (default で 0)
template <typename Container>
vector<int> wildcard_pattern_matching(
    const Container& a, const Container& b,
    const typename Container::value_type& wildcard = 0) {
  if ((int)b.size() == 0) return vector<int>(a.size() + 1, 1);
  if (a.size() < b.size()) return {};
  vector<int> res1 = inner<Container, 998244353>(a, b, wildcard);
  vector<int> res2 = inner<Container, 924844033>(a, b, wildcard);
  vector<int> res3 = inner<Container, 1012924417>(a, b, wildcard);
  for (int i = 0; i < (int)res1.size(); i++) res1[i] &= res2[i] & res3[i];
  return res1;
}

}  // namespace WildcardPatternMatchingImpl

using WildcardPatternMatchingImpl::wildcard_pattern_matching;

/**
 * @brief Wildcard Pattern Matching
 */


void q() {
  ini(N, M);
  ins(S1, S2);

  auto wpm = wildcard_pattern_matching(S1, S2, '?');

  trc(S1);
  trc(S2);
  trc(wpm);

  string U;
  each(c, S1) U.push_back(c == '?' ? 'a' : c);
  each(c, S2) U.push_back(c);
  StringSearch ss{U};

  auto comp = [&](vp a, vp b) {
    reverse(all(a)), reverse(all(b));
    while (sz(a)) {
      assert(sz(b));
      auto p = a.back();
      auto q = b.back();
      int m = min(p.se - p.fi, q.se - q.fi);
      a.back().fi += m;
      b.back().fi += m;
      if (a.back().fi == a.back().se) a.pop_back();
      if (b.back().fi == b.back().se) b.pop_back();
      int c = ss.strcmp(p.fi, p.fi + m, q.fi, q.fi + m);
      if (c != 0) return c < 0;
    }
    return false;
  };

  pair<int, vp> ans{-1, {}};
  rep(i, N - M + 1) {
    if (wpm[i] == 1) {
      vp v;
      v.emplace_back(0, i);
      v.emplace_back(N, N + M);
      v.emplace_back(i + M, N);
      if (ans.fi == -1 or comp(v, ans.se)) {
        ans = {i, v};
      }
    }
  }
  if (ans.fi == -1) {
    out(-1);
  } else {
    int i = ans.fi;
    rep(j, M) S1[j + i] = S2[j];
    rep(j, N) if (S1[j] == '?') S1[j] = 'a';
    out(S1);
  }
}

void Nyaan::solve() {
  int t = 1;
  in(t);
  while (t--) q();
}