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;
  constexpr long long MAXN = 200000;
  constexpr long long MAXFACT = MAXN * 2 + 5;
  constexpr long long MOD = 998244353;
  pair<long long, long long> arr[MAXN];
  struct fenwick {
    constexpr static long long FWSIZE = MAXN + 5;
    long long arr[FWSIZE];
    long long query(long long index) const {
      long long ans = 0;
      for (; index > 0; index -= index & -index) {
        ans += arr[index];
      }
      return ans;
    }
    void update(long long index, long long inc) {
      for (; index < FWSIZE; index += index & -index) {
        arr[index] += inc;
      }
    }
  } fw;
  template <typename Callback>
  long long bsta(long long low, long long high, Callback cb) {
    while (low + 1 < high) {
      long long mid = (low + high) / 2;
      if (cb(mid)) {
        low = mid;
      } else {
        high = mid;
      }
    }
    return high;
  }
  long long facts[MAXFACT], invfacts[MAXFACT];
  long long powmod(long long base, long long e) {
    if (e == 0) return 1;
    long long tmp = powmod(base, e / 2);
    tmp *= tmp;
    tmp %= MOD;
    if (e & 1) {
      tmp *= base;
      tmp %= MOD;
    }
    return tmp;
  }
  long long combin(long long n, long long a, long long b) {
    return (((facts[n] * invfacts[a]) % MOD) * invfacts[b]) % MOD;
  }
  long long cache[MAXN];
  int32_t main() {
    ios_base::sync_with_stdio(false);
    {
      long long cum = 1;
      facts[0] = invfacts[0] = cum;
      for (long long i = 1; i < MAXFACT; ++i) {
        cum *= i;
        cum %= MOD;
        facts[i] = cum;
        invfacts[i] = powmod(facts[i], MOD - 2);
      }
    }
    long long t;
    cin >> t;
    for (long long c = 0; c < t; ++c) {
      long long n, m;
      cin >> n >> m;
      for (long long i = 0; i < m; ++i) {
        cin >> arr[i].first >> arr[i].second;
      }
      long long splits = 0;
      long long* cache_end = cache;
      for (long long i = m - 1; i >= 0; --i) {
        const long long target = arr[i].second;
        long long realidx = bsta(
            0, n, [&](long long test) { return test - fw.query(test) < target; });
        if (fw.query(realidx + 1) == fw.query(realidx)) {
          ++splits;
        }
        fw.update(realidx, 1);
        *cache_end++ = realidx;
      }
      long long tmp = n - 1 - splits;
      cout << combin(n + tmp, n, tmp) << '\n';
      while (cache_end != cache) {
        --cache_end;
        fw.update(*cache_end, -1);
      }
    }
  }
  