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;
  template <typename T>
  bool chkmax(T &x, T y) {
    return x < y ? x = y, true : false;
  }
  template <typename T>
  bool chkmin(T &x, T y) {
    return x > y ? x = y, true : false;
  }
  int readint() {
    int x = 0, f = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9') {
      if (ch == '-') f = -1;
      ch = getchar();
    }
    while (ch >= '0' && ch <= '9') {
      x = x * 10 + ch - '0';
      ch = getchar();
    }
    return x * f;
  }
  const int cys = 998244353, N = 400000;
  int n, m, rt, ncnt;
  mt19937 mrand(23984);
  int ch[200005][2], sum[200005], siz[200005], val[200005];
  long long fac[400005], inv[400005];
  long long qpow(long long x, long long p) {
    long long ret = 1;
    for (; p; p >>= 1, x = x * x % cys)
      if (p & 1) ret = ret * x % cys;
    return ret;
  }
  void update(int u) {
    siz[u] = 1 + siz[ch[u][0]] + siz[ch[u][1]];
    sum[u] = val[u] + sum[ch[u][0]] + sum[ch[u][1]];
  }
  void split(int u, int k, int &x, int &y) {
    if (!u) return (void)(x = y = 0);
    if (sum[ch[u][0]] + val[u] <= k)
      x = u, split(ch[u][1], k - sum[ch[u][0]] - val[u], ch[x][1], y);
    else
      y = u, split(ch[u][0], k, x, ch[y][0]);
    update(u);
  }
  int merge(int x, int y) {
    if (!x || !y) return x + y;
    if (mrand() % (siz[x] + siz[y]) < siz[x]) {
      ch[x][1] = merge(ch[x][1], y);
      update(x);
      return x;
    } else {
      ch[y][0] = merge(x, ch[y][0]);
      update(y);
      return y;
    }
  }
  int main() {
    int T = readint();
    fac[0] = inv[0] = 1;
    for (int i = 1; i <= N; i++) fac[i] = fac[i - 1] * i % cys;
    inv[N] = qpow(fac[N], cys - 2);
    for (int i = N - 1; i >= 1; i--) inv[i] = inv[i + 1] * (i + 1) % cys;
    while (T--) {
      n = readint();
      m = readint();
      rt = ncnt = 0;
      int x, y;
      for (int i = 1; i <= m; i++) {
        x = readint();
        y = readint();
        if (y > sum[rt]) {
          ncnt++;
          val[ncnt] = sum[ncnt] = y - sum[rt] + 1, siz[ncnt] = 1,
          ch[ncnt][0] = ch[ncnt][1] = 0;
          rt = merge(rt, ncnt);
        } else {
          int a, b, c, to;
          split(rt, y - 1, a, b);
          to = b;
          while (ch[to][0]) to = ch[to][0];
          split(b, val[to], b, c);
          if (sum[a] + val[b] == y)
            val[b]++, sum[b]++, rt = merge(a, merge(b, c));
          else {
            ncnt++;
            val[ncnt] = sum[ncnt] = y - sum[a] + 1, siz[ncnt] = 1,
            ch[ncnt][0] = ch[ncnt][1] = 0;
            val[b] = sum[b] = sum[a] + val[b] - y;
            rt = merge(a, merge(merge(ncnt, b), c));
          }
        }
      }
      int num = n - 1 - siz[rt];
      printf("%lld\n", fac[n + num] * inv[n] % cys * inv[num] % cys);
    }
    return 0;
  }
  