description: Mocha wants to be an astrologer. There are n stars which can be seen in Zhijiang, and the brightness of the i-th star is a_i. 
  
  Mocha considers that these n stars form a constellation, and she uses (a_1,a_2,…,a_n) to show its state. A state is called mathematical if all of the following three conditions are satisfied:
  
    * For all i (1≤ i≤ n), a_i is an integer in the range [l_i, r_i].
    * ∑  _{i=1} ^ n a_i ≤ m.
    * \gcd(a_1,a_2,…,a_n)=1.
  
  
  
  Here, \gcd(a_1,a_2,…,a_n) denotes the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers a_1,a_2,…,a_n.
  
  Mocha is wondering how many different mathematical states of this constellation exist. Because the answer may be large, you must find it modulo 998 244 353.
  
  Two states (a_1,a_2,…,a_n) and (b_1,b_2,…,b_n) are considered different if there exists i (1≤ i≤ n) such that a_i ≠ b_i.
  
  Input
  
  The first line contains two integers n and m (2 ≤ n ≤ 50, 1 ≤ m ≤ 10^5) — the number of stars and the upper bound of the sum of the brightness of stars.
  
  Each of the next n lines contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the range of the brightness of the i-th star.
  
  Output
  
  Print a single integer — the number of different mathematical states of this constellation, modulo 998 244 353.
  
  Examples
  
  Input
  
  
  2 4
  1 3
  1 2
  
  
  Output
  
  
  4
  
  Input
  
  
  5 10
  1 10
  1 10
  1 10
  1 10
  1 10
  
  
  Output
  
  
  251
  
  Input
  
  
  5 100
  1 94
  1 96
  1 91
  4 96
  6 97
  
  
  Output
  
  
  47464146
  
  Note
  
  In the first example, there are 4 different mathematical states of this constellation:
  
    * a_1=1, a_2=1.
    * a_1=1, a_2=2.
    * a_1=2, a_2=1.
    * a_1=3, a_2=1.
solution: #include <bits/stdc++.h>
  using namespace std;
  using ll = long long;
  void setIO(string name = "") {
    cin.tie(0)->sync_with_stdio(0);
    if ((int)name.size()) {
      freopen((name + ".in").c_str(), "r", stdin);
      freopen((name + ".out").c_str(), "w", stdout);
    }
  }
  void __print(int x) { cerr << x; }
  void __print(long x) { cerr << x; }
  void __print(long long x) { cerr << x; }
  void __print(unsigned x) { cerr << x; }
  void __print(unsigned long x) { cerr << x; }
  void __print(unsigned long long x) { cerr << x; }
  void __print(float x) { cerr << x; }
  void __print(double x) { cerr << x; }
  void __print(long double x) { cerr << x; }
  void __print(char x) { cerr << '\'' << x << '\''; }
  void __print(const char *x) { cerr << '\"' << x << '\"'; }
  void __print(const string &x) { cerr << '\"' << x << '\"'; }
  void __print(bool x) { cerr << (x ? "true" : "false"); }
  template <typename T, typename V>
  void __print(const pair<T, V> &x) {
    cerr << '{';
    __print(x.first);
    cerr << ',';
    __print(x.second);
    cerr << '}';
  }
  template <typename T>
  void __print(const T &x) {
    int f = 0;
    cerr << '{';
    for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
    cerr << "}";
  }
  void _print() { cerr << "]\n"; }
  template <typename T, typename... V>
  void _print(const T &t, const V &...v) {
    __print(t);
    if (sizeof...(v)) cerr << ", ";
    _print(v...);
  }
  const long long N = 1e5 + 10;
  const long long mod = 998244353;
  long long n, m;
  long long dp[55][N];
  long long f[N];
  long long l[55], r[55];
  long long l1[55], r1[55];
  long long construct_f(long long m) {
    for (long long i = 0; i < (n + 1); ++i) {
      for (long long j = 0; j < (m + 1); ++j) {
        dp[i][j] = 0;
      }
    }
    dp[0][0] = 1;
    for (ll i = 0; i < n; i++) {
      ll r = 0;
      for (ll j = 0; j <= m; j++) {
        if (j >= l1[i]) {
          r += dp[i][j - l1[i]];
          if (r >= mod) r -= mod;
        }
        dp[i + 1][j] = r;
        if (j >= r1[i]) {
          r -= dp[i][j - r1[i]];
          if (r < 0) r += mod;
        }
      }
    }
    long long res = 0;
    for (long long j = 0; j <= m; ++j) {
      res += dp[n][j];
    }
    return res % mod;
  }
  void solve() {
    cin >> n >> m;
    for (long long i = 0; i < (n); ++i) {
      cin >> l[i] >> r[i];
    }
    for (long long i = 1; i < (m + 1); ++i) {
      long long max_l = -1;
      for (long long j = 0; j < (n); ++j) {
        l1[j] = 1e9, r1[j] = -1;
        for (long long k = i; k <= m; k += i) {
          if (l[j] <= k && k <= r[j]) {
            l1[j] = min(l1[j], k);
            r1[j] = k;
          }
        }
        max_l = max(max_l, l1[j]);
      }
      if (max_l == 1e9) {
        f[i] = 0;
      } else {
        for (long long j = 0; j < (n); ++j) {
          l1[j] /= i, r1[j] /= i;
        }
        f[i] = construct_f(m / i);
      }
    }
    for (long long i = m; i > 0; i--) {
      for (long long j = 2 * i; j <= m; j += i) {
        f[i] -= f[j];
        if (f[i] < 0) {
          f[i] += mod;
        }
      }
    }
    cout << f[1] << "\n";
  }
  signed main() {
    setIO();
    long long t = 1;
    while (t--) solve();
    return 0;
  }
  