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 N, M;
  const int MAXN = 2e5 + 10;
  int les[MAXN];
  struct TreeArray {
    int f[MAXN];
    void update(int x, int d) {
      while (x <= N) f[x] += d, x += x & (-x);
    }
    int query(int x) {
      int ret = 0;
      while (x) ret += f[x], x -= x & (-x);
      return ret;
    }
    int find(int x) {
      int L = 0, R = N, mid;
      while (L + 1 < R) {
        mid = (L + R) >> 1;
        int tmp = query(mid);
        if (mid - tmp < x)
          L = mid;
        else
          R = mid;
      }
      return R;
    }
  } tr;
  int p[MAXN], q[MAXN];
  long long fact[MAXN << 1], invfact[MAXN << 1];
  const long long mod = 998244353;
  long long fastpow(long long a, long long b) {
    long long ret = 1;
    while (b) {
      if (b & 1) ret = ret * a % mod;
      a = a * a % mod;
      b >>= 1;
    }
    return ret;
  }
  int cnt;
  int s[MAXN], n;
  int main() {
    fact[0] = fact[1] = 1;
    for (int i = 2; i <= 400000; i++) fact[i] = fact[i - 1] * i % mod;
    invfact[400000] = fastpow(fact[400000], mod - 2);
    for (int i = 399999; i >= 0; i--) invfact[i] = invfact[i + 1] * (i + 1) % mod;
    for (int i = 1; i <= 200000; i++) les[i] = -1;
    int T;
    scanf("%d", &T);
    while (T--) {
      scanf("%d%d", &N, &M);
      cnt = N - 1;
      n = 0;
      if (M) {
        for (int i = 1; i <= M; i++) scanf("%d%d", &p[i], &q[i]);
        for (int i = M, last = N + 1, pos; i >= 1; i--) {
          if (last > p[i] + 1) {
            pos = tr.find(p[i] + 1);
            s[++n] = pos;
            if (les[pos - 1] == -1) les[pos - 1] = 0;
            tr.update(pos, 1);
          }
          pos = tr.find(q[i]);
          if (les[pos - 1] == -1) les[pos - 1] = 0;
          if (les[pos] == -1) les[pos] = 1, --cnt;
          tr.update(pos, 1);
          s[++n] = pos;
          last = p[i];
        }
        for (int i = 1; i <= n; i++)
          tr.update(s[i], -1), les[s[i] - 1] = les[s[i]] = -1;
      }
      printf("%lld\n", fact[N + cnt] * invfact[N] % mod * invfact[cnt] % mod);
    }
    return 0;
  }
  