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;
  const int MAXN = (int)4e5 + 5;
  const int MOD = 998244353;
  const int K = 3500;
  const int M = 60;
  const long long S = (1ll << M) - 1;
  int addMod(int a, int b, int m = MOD) { return a + b < m ? a + b : a + b - m; }
  int mulMod(int a, int b, int m = MOD) { return a * 1ll * b % m; }
  int binPow(int a, int b, int m = MOD) {
    int ret = 1;
    while (b > 0) {
      if (b & 1) {
        ret = mulMod(ret, a, m);
      }
      a = mulMod(a, a, m);
      b >>= 1;
    }
    return ret;
  }
  int fact[MAXN], inv[MAXN];
  int n, m;
  void pre() {
    fact[0] = 1;
    for (int i = (1); i < (MAXN); ++i) {
      fact[i] = mulMod(fact[i - 1], i);
    }
    inv[MAXN - 1] = binPow(fact[MAXN - 1], MOD - 2);
    for (int i = MAXN - 1; i; --i) {
      inv[i - 1] = mulMod(inv[i], i);
    }
  }
  int C(int n, int k) { return mulMod(fact[n], mulMod(inv[k], inv[n - k])); }
  bool bit(long long x, int p) { return x & (1ll << p); }
  long long B[K + 1];
  void solve() {
    cin >> n >> m;
    fill(B, B + K + 1, 0ll);
    for (int i = (0); i < (m); ++i) {
      int x, y;
      cin >> x >> y;
      --y;
      int idx = y / M;
      y %= M;
      B[idx] |= (1ll << y);
      for (int j = K - 1; j > idx; --j) {
        B[j + 1] |= bit(B[j], M - 1);
        B[j] = ((B[j] << 1) & S);
      }
      long long a = (B[idx] & ((1ll << y) - 1));
      long long b = (B[idx] ^ a);
      B[idx + 1] |= bit(b, M - 1);
      B[idx] = ((a + (b << 1)) & S);
    }
    int cnt = n - 1;
    for (int i = (0); i < (K); ++i) {
      cnt -= __builtin_popcountll(B[i]);
    }
    int ans = C(n + cnt, n);
    cout << ans << '\n';
  }
  int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int tt = 1;
    cin >> tt;
    pre();
    for (int i = 1; i <= tt; ++i) {
      solve();
    }
    return 0;
  }
  