description: Consider the insertion sort algorithm used to sort an integer sequence [a_1, a_2, …, a_n] of length n in non-decreasing order.
  
  For each i in order from 2 to n, do the following. If a_i ≥ a_{i-1}, do nothing and move on to the next value of i. Otherwise, find the smallest j such that a_i < a_j, shift the elements on positions from j to i-1 by one position to the right, and write down the initial value of a_i to position j. In this case we'll say that we performed an insertion of an element from position i to position j.
  
  It can be noticed that after processing any i, the prefix of the sequence [a_1, a_2, …, a_i] is sorted in non-decreasing order, therefore, the algorithm indeed sorts any sequence.
  
  For example, sorting [4, 5, 3, 1, 3] proceeds as follows: 
  
    * i = 2: a_2 ≥ a_1, do nothing; 
    * i = 3: j = 1, insert from position 3 to position 1: [3, 4, 5, 1, 3]; 
    * i = 4: j = 1, insert from position 4 to position 1: [1, 3, 4, 5, 3]; 
    * i = 5: j = 3, insert from position 5 to position 3: [1, 3, 3, 4, 5]. 
  
  
  
  You are given an integer n and a list of m integer pairs (x_i, y_i). We are interested in sequences such that if you sort them using the above algorithm, exactly m insertions will be performed: first from position x_1 to position y_1, then from position x_2 to position y_2, ..., finally, from position x_m to position y_m.
  
  How many sequences of length n consisting of (not necessarily distinct) integers between 1 and n, inclusive, satisfy the above condition? Print this number modulo 998 244 353.
  
  Input
  
  Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^5). Description of the test cases follows.
  
  The first line of each test case contains two integers n and m (2 ≤ n ≤ 2 ⋅ 10^5; 0 ≤ m < n) — the length of the sequence and the number of insertions.
  
  The i-th of the following m lines contains two integers x_i and y_i (2 ≤ x_1 < x_2 < … < x_m ≤ n; 1 ≤ y_i < x_i). These lines describe the sequence of insertions in chronological order.
  
  It is guaranteed that the sum of m over all test cases does not exceed 2 ⋅ 10^5. Note that there is no constraint on the sum of n of the same kind.
  
  Output
  
  For each test case, print the number of sequences of length n consisting of integers from 1 to n such that sorting them with the described algorithm produces the given sequence of insertions, modulo 998 244 353.
  
  Example
  
  Input
  
  
  3
  3 0
  3 2
  2 1
  3 1
  5 3
  3 1
  4 1
  5 3
  
  
  Output
  
  
  10
  1
  21
  
  Note
  
  In the first test case, the algorithm performs no insertions — therefore, the initial sequence is already sorted in non-decreasing order. There are 10 such sequences: [1, 1, 1], [1, 1, 2], [1, 1, 3], [1, 2, 2], [1, 2, 3], [1, 3, 3], [2, 2, 2], [2, 2, 3], [2, 3, 3], [3, 3, 3].
  
  In the second test case, the only sequence satisfying the conditions is [3, 2, 1].
  
  In the third test case, [4, 5, 3, 1, 3] is one of the sought sequences.
solution: #include <bits/stdc++.h>
  using namespace std;
  int abc;
  int rd(int l, int r) { return rand() % (r - l + 1) + l; }
  const int mxn = 2e5 + 3, mod = 998244353;
  long long por(long long x, int y = mod - 2) {
    long long r = 1;
    for (; y; y >>= 1) {
      if (y & 1) r = r * x % mod;
      x = x * x % mod;
    }
    return r;
  }
  int n, m, nn, b[mxn][2], d[mxn];
  long long jc[mxn * 2], inv[mxn * 2];
  struct zZz {
    int a[mxn], tk[mxn], nn;
    void add(int x) {
      tk[++nn] = x;
      for (; x <= n; x += x & -x) ++a[x];
    }
    int ask(int k) {
      int p = 0, z = 0;
      for (int i = 1 << 17; i; i >>= 1) {
        if (p + i > n) continue;
        p += i;
        if (p - z - a[p] >= k)
          p -= i;
        else
          z += a[p];
      }
      return p + 1;
    }
    void clr() {
      while (nn) {
        int x = tk[nn--];
        for (; x <= n; x += x & -x) a[x] = 0;
      }
    }
  } ar;
  set<int> st;
  long long C(int x, int y) { return jc[x] * inv[y] % mod * inv[x - y] % mod; }
  int main() {
    n = 2 * mxn - 1;
    jc[0] = inv[0] = 1;
    for (int i = 1; i <= n; ++i) jc[i] = jc[i - 1] * i % mod;
    inv[n] = por(jc[n]);
    for (int i = n - 1; i; --i) inv[i] = inv[i + 1] * (i + 1) % mod;
    int ca;
    abc = scanf("%d", &ca);
    while (ca--) {
      ar.clr();
      abc = scanf("%d%d", &n, &m);
      for (int i = 1; i <= m; ++i) abc = scanf("%d%d", &b[i][0], &b[i][1]);
      b[m + 1][0] = n + 1;
      if (b[1][0] != 1)
        b[0][0] = b[0][1] = 1;
      else
        b[0][0] = 0;
      nn = 0;
      int ls = n + 1, nm = 0;
      st.clear();
      d[n + 1] = -1;
      for (int t = m; ~t && b[t][0]; --t) {
        int x = b[t][0], y = b[t][1], k = ar.ask(y), k2 = ar.ask(x + 1),
            xx = b[t + 1][0];
        ar.add(k);
        d[k] = x;
        st.insert(k);
        if (x + 1 != xx) {
          while (st.size() && *--st.end() > k2) {
            auto it = --st.end();
            k = *it;
            if (k + 1 == ls)
              nm += d[k] > d[k + 1];
            else
              nm += xx - 1 > d[ls], xx -= ls - k + 1, nm += d[k] > xx;
            ls = k;
            st.erase(it);
          }
          nm += xx - 1 > d[ls];
          ls = k2, d[k2] = x + 1;
        }
      }
      for (int i = ls - 1; i; --i) nm += d[i] > d[i + 1];
      printf("%lld\n", C(2 * n - nm, n));
    }
    return 0;
  }
  