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 = 6e5 + 5;
  const int MOD = 998244353;
  long long q_pow(long long a, long long b, long long p = MOD) {
    long long ret = 1;
    for (; b; a = a * a % p, b >>= 1)
      if (b & 1) ret = ret * a % p;
    return ret;
  }
  long long q_inv(long long x, long long p = MOD) { return q_pow(x, p - 2, p); }
  int fac[MAXN], ifac[MAXN];
  void build(int n) {
    fac[0] = 1;
    for (int i = 1; i <= n; ++i) fac[i] = 1ll * fac[i - 1] * i % MOD;
    ifac[n] = q_inv(fac[n]);
    for (int i = n - 1; i >= 0; --i) ifac[i] = 1ll * ifac[i + 1] * (i + 1) % MOD;
  }
  int binom(int n, int m) {
    return 1ull * fac[n] * ifac[m] % MOD * ifac[n - m] % MOD;
  }
  int T, N, M, D;
  set<int> S;
  int rt, ls[MAXN], rs[MAXN], val[MAXN], key[MAXN], siz[MAXN], Tlen, tag[MAXN];
  int newnode(int v) {
    int p = ++Tlen;
    val[p] = v, key[p] = rand(), siz[p] = 1, ls[p] = rs[p] = 0, tag[p] = 0;
    return p;
  }
  void pushup(int x) { siz[x] = siz[ls[x]] + siz[rs[x]] + 1; }
  void cov(int o, int k) {
    if (o) val[o] += k, tag[o] += k;
  }
  void pushdown(int o) {
    if (tag[o]) cov(ls[o], tag[o]), cov(rs[o], tag[o]), tag[o] = 0;
  }
  void split(int now, int k, int& x, int& y) {
    if (!now) {
      x = y = 0;
      return;
    }
    pushdown(now);
    if (val[now] <= k)
      x = now, split(rs[now], k, rs[now], y);
    else
      y = now, split(ls[now], k, x, ls[now]);
    pushup(now);
  }
  int merge(int x, int y) {
    if (!x || !y) return x | y;
    pushdown(x), pushdown(y);
    if (key[x] > key[y]) {
      rs[x] = merge(rs[x], y), pushup(x);
      return x;
    } else {
      ls[y] = merge(x, ls[y]), pushup(y);
      return y;
    }
  }
  int main() {
    build(400000);
    scanf("%d", &T);
    while (T--) {
      scanf("%d%d", &N, &M);
      int x, y, r1, r2, r3, r4, cnt = 0;
      Tlen = 0;
      rt = 0;
      for (int i = 1; i <= M; ++i) {
        scanf("%d%d", &x, &y);
        split(rt, y - 1, r1, r2);
        split(r2, y, r3, r4);
        if (r3)
          r2 = merge(r3, r4), cov(r2, 1), rt = merge(r1, r2);
        else
          r2 = merge(newnode(y), r4), cov(r2, 1), rt = merge(r1, r2), ++cnt;
      }
      printf("%d\n", binom(N - cnt + N - 1, N));
    }
    return 0;
  }
  