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;
  static char ibuf[1 << 20];
  char *fis = ibuf, *fit = ibuf;
  inline char readChar() {
    return fis == fit && (fit = (fis = ibuf) + fread(ibuf, 1, 1 << 20, stdin),
                          fis == fit)
               ? EOF
               : *fis++;
  }
  inline int read() {
    char c;
    int x;
    for (c = readChar(); !isdigit(c); c = readChar())
      ;
    for (x = 0; isdigit(c); c = readChar()) {
      x = x * 10 + c - '0';
    }
    return x;
  }
  static char ostc[100], obuf[1 << 20];
  int ol = 0;
  char *fos = obuf, *fot = obuf + (1 << 20) - 1;
  inline void writeChar(char c) {
    *fos++ = c;
    if (fos == fot) {
      fwrite(obuf, 1, fos - obuf, stdout);
      fos = obuf;
    }
  }
  inline void write(int n, char c) {
    if (!n) {
      writeChar('0');
    } else {
      while (n) {
        ostc[++ol] = n % 10 + 48, n /= 10;
      }
    }
    for (; ol; ol--) {
      writeChar(ostc[ol]);
    }
    writeChar(c);
  }
  const int N = 1 << 20;
  const int mod = 998244353;
  int jc[N + 1], ny[N + 1], s[N + 1];
  int C(int n, int m) {
    if (n < m) return 0;
    return 1LL * jc[n] * ny[m] % mod * ny[n - m] % mod;
  }
  int qpow(int x, int times) {
    int res = 1;
    while (times) {
      if (times & 1) res = 1LL * res * x % mod;
      times >>= 1;
      x = 1LL * x * x % mod;
    }
    return res;
  }
  inline int lowbit(int x) { return x & (-x); }
  void add(int pos, int x) {
    while (pos <= N) {
      s[pos] += x;
      pos += lowbit(pos);
    }
  }
  int x[N], y[N];
  int main() {
    jc[0] = 1;
    ny[0] = 1;
    for (int i = 1; i <= N; i++) jc[i] = 1LL * jc[i - 1] * i % mod;
    for (int i = 1; i <= N; i++) ny[i] = qpow(jc[i], mod - 2);
    int T = read();
    while (T--) {
      int n = read();
      int m = read();
      set<int> st;
      vector<int> w;
      for (int i = 1; i <= m; i++) {
        x[i] = read();
        y[i] = read();
      }
      int k = n - 1;
      for (int i = m; i >= 1; i--) {
        int p = y[i];
        int L = 0, R = N;
        while (L + 1 < R) {
          int mid = L + R >> 1;
          if (mid - L - s[mid] < p) {
            p -= mid - L - s[mid];
            L = mid;
          } else
            R = mid;
        }
        int ans = L + 1;
        add(ans, 1);
        w.push_back(ans);
        if (ans < n && !st.count(ans + 1)) k--;
        st.insert(ans);
      }
      printf("%d\n", C(n + k, n));
      for (int x : w) add(x, -1);
    }
    return 0;
  }
  