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;
  mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
  long long int abss(long long int a) {
    if (a < 0) return -a;
    return a;
  }
  long long int ones(long long int a) {
    long long int cnt = 0;
    while (a > 0) {
      if (a & 1) cnt++;
      a >>= 1;
    }
    return cnt;
  }
  long long int fast_pow(long long int b, long long int e,
                         long long int width = 998244353) {
    if (e == 0) {
      return 1;
    } else if (e == 1) {
      return b % width;
    }
    b = b % width;
    long long int ans = 1;
    while (e > 0) {
      if ((e & 1) == 1) {
        ans = (ans * b) % width;
      }
      e >>= 1;
      b = (b * b) % width;
    }
    return ans;
  }
  long long int mod_inv(long long int a, long long int width = 998244353) {
    return fast_pow(a, width - 2, width);
  }
  template <typename Number, Number width>
  class ModularArithmetic {
   private:
    Number n;
  
   public:
    friend ostream &operator<<(ostream &os, ModularArithmetic const &num) {
      return os << num.n;
    }
    friend istream &operator>>(istream &is, ModularArithmetic &num) {
      is >> num.n;
      return is;
    }
    ModularArithmetic() : n(0) {}
    ModularArithmetic(Number n) : n(n % width) {
      if (this->n < 0) this->n += width;
    }
    Number get() const { return n; }
    ModularArithmetic operator+(const ModularArithmetic &b) {
      Number t = (n + b.get()) % width;
      if (t < 0) return ModularArithmetic(width + t);
      return ModularArithmetic(t);
    }
    ModularArithmetic operator-(const ModularArithmetic &b) {
      Number t = (n - b.get()) % width;
      if (t < 0) return ModularArithmetic(width + t);
      return ModularArithmetic(t);
    }
    ModularArithmetic operator*(const ModularArithmetic &b) {
      Number t = (n * b.get()) % width;
      if (t < 0) return ModularArithmetic(width + t);
      return ModularArithmetic(t);
    }
    ModularArithmetic operator/(const ModularArithmetic &b) {
      assert(b.get() != 0);
      Number ans = n * mod_inv(b.get(), width);
      if ((ans) < 0) return ModularArithmetic(width + (ans) % width);
      return ModularArithmetic(ans % width);
    }
    ModularArithmetic &operator+=(const ModularArithmetic &b) {
      n = (n + b.get()) % width;
      if (n < 0) n = n + width;
      return *this;
    }
    ModularArithmetic &operator-=(const ModularArithmetic &b) {
      n = (n - b.get()) % width;
      if (n < 0) n = n + width;
      return *this;
    }
    ModularArithmetic &operator*=(const ModularArithmetic &b) {
      n = (n * b.get()) % width;
      if (n < 0) n = n + width;
      return *this;
    }
    ModularArithmetic &operator/=(const ModularArithmetic &b) {
      assert(b.get() != 0);
      n = (n * mod_inv(b.get(), width)) % width;
      if (n < 0) n = n + width;
      return *this;
    }
  };
  template <class T, size_t N>
  ostream &operator<<(ostream &os, const array<T, N> &p) {
    os << "<";
    for (auto &it : p) os << it << " ";
    return os << ">";
  }
  template <class S, class T>
  ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << "(" << p.first << "," << p.second << ")";
  }
  template <class S, class T>
  istream &operator>>(istream &is, pair<S, T> &p) {
    return is >> p.first >> p.second;
  }
  template <class T>
  ostream &operator<<(ostream &os, const vector<T> &p) {
    os << "[";
    for (auto &it : p) os << it << " ";
    return os << "]";
  }
  template <class T, typename Cmp>
  ostream &operator<<(ostream &os, const set<T, Cmp> &p) {
    os << "[";
    for (auto &it : p) os << it << " ";
    return os << "]";
  }
  template <class T>
  ostream &operator<<(ostream &os, const multiset<T> &p) {
    os << "[";
    for (auto &it : p) os << it << " ";
    return os << "]";
  }
  template <class S, class T, typename Cmp>
  ostream &operator<<(ostream &os, const map<S, T, Cmp> &p) {
    os << "[";
    for (auto &it : p) os << it << " ";
    return os << "]";
  }
  template <class S, class T>
  istream &operator>>(istream &is, const pair<S, T> &p) {
    return is >> p.first >> p.second;
  }
  template <class T>
  istream &operator>>(istream &is, vector<T> &p) {
    for (auto &itr : p) is >> itr;
    return is;
  }
  template <class T>
  void dbs(string str, T t) {
    cerr << str << ":" << t << "\n";
  }
  template <class T, class... S>
  void dbs(string str, T t, S... second) {
    long long int idx = str.find(',');
    cerr << str.substr(0, idx) << ":" << t << ",";
    dbs(str.substr(idx + 1), second...);
  }
  bool isComposite(long long int a, long long int d, long long int n) {
    long long int res = fast_pow(a, d, n);
    if (res == 1 || res == n - 1) return false;
    while (d != (n - 1)) {
      res = (res * res) % n;
      if (res == n - 1) {
        return false;
      }
    }
    return true;
  }
  bool MillerRabinDet(long long int n) {
    if (n < 4) return n == 2 || n == 3;
    long long int d = n - 1;
    while (d & 1 == 0) {
      d >>= 1;
    }
    for (long long int a : {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}) {
      if (a == n) return true;
      if (isComposite(a, d, n)) {
        return false;
      }
    }
    return true;
  }
  bool MillerRabinNonDet(long long int n, long long int k = 1000) {
    if (n < 4) return n == 2 || n == 3;
    long long int d = n - 1;
    long long int second = 0;
    while (d & 1 == 0) {
      d >>= 1;
      second++;
    }
    long long int a;
    for (long long int i = 0; i < k; i++) {
      a = 2 + rand() % (n - 3);
      if (isComposite(a, d, n)) {
        return false;
      }
    }
    return true;
  }
  long long int gcd(long long int a, long long int b) {
    if (a % b == 0) return b;
    return gcd(b, a % b);
  }
  long long int n, m;
  vector<pair<long long int, long long int>> arr;
  vector<long long int> sieve;
  vector<long long int> prime;
  vector<long long int> mu;
  const long long int sz = 100005;
  ModularArithmetic<long long int, 998244353> compute(long long int d) {
    long long int dm = m / d;
    vector<ModularArithmetic<long long int, 998244353>> dp1(dm + 1, 0),
        dp2(dm + 1, 0);
    dp1[0] = 1;
    for (long long int i = 0; i < n; i++) {
      long long int lf = (arr[i].first + d - 1) / d;
      long long int rt = (arr[i].second) / d;
      if (lf > rt) return 0;
      dp2[0] = dp1[0];
      for (long long int j = 1; j <= dm; j++) dp2[j] = dp1[j] + dp2[j - 1];
      {};
      for (long long int j = 0; j <= dm; j++) {
        dp1[j] =
            ((j - lf >= 0) ? dp2[j - lf]
                           : ModularArithmetic<long long int, 998244353>(0)) -
            (((j - (rt + 1)) >= 0)
                 ? dp2[j - (rt + 1)]
                 : ModularArithmetic<long long int, 998244353>(0));
      }
    }
    ModularArithmetic<long long int, 998244353> ans = 0;
    for (auto itr : dp1) ans += itr;
    ans -= dp1[0];
    return ans;
  }
  ModularArithmetic<long long int, 998244353> cal(int d) {
    int dm = m / d;
    vector<ModularArithmetic<long long int, 998244353>> dp1(dm + 1, 0);
    dp1[0] = 1;
    vector<ModularArithmetic<long long int, 998244353>> dp2(dm + 1, 0);
    for (int i = 1; i <= dm; i++) dp1[i] = 0;
    for (int i = 0; i < n; i++) {
      int L = (arr[i].first + d - 1) / d, R = arr[i].second / d;
      if (L > R) return ModularArithmetic<long long int, 998244353>(0);
      for (int j = 0; j <= dm; j++)
        dp2[j] = (dp1[j] + (j ? dp2[j - 1]
                              : ModularArithmetic<long long int, 998244353>(0)));
      for (int j = 0; j <= dm; j++) {
        dp1[j] = ((j - L >= 0 ? dp2[j - L]
                              : ModularArithmetic<long long int, 998244353>(0)) -
                  (j - R - 1 >= 0 ? dp2[j - R - 1] : 0));
      }
    }
    ModularArithmetic<long long int, 998244353> ans = 0;
    for (int i = 1; i <= dm; i++) ans = (ans + dp1[i]);
    return ans;
  }
  void solve() {
    sieve.assign(sz + 1, 1);
    mu.assign(sz + 1, 0);
    mu[1] = 1;
    prime.clear();
    sieve[0] = sieve[1] = 0;
    for (long long int i = 2; i <= sz; i++) {
      if (sieve[i]) {
        prime.push_back(i);
        mu[i] = -1;
      }
      for (long long int j = 0; j < prime.size() && i * prime[j] <= sz; j++) {
        sieve[i * prime[j]] = 0;
        if (i % prime[j] == 0) {
          mu[i * prime[j]] = 0;
          break;
        } else {
          mu[i * prime[j]] = mu[i] * mu[prime[j]];
        }
      }
    }
    cin >> n >> m;
    vector<pair<long long int, long long int>>(n).swap(arr);
    for (long long int i = 0; i < n; ++i) cin >> arr[i].first >> arr[i].second;
    ModularArithmetic<long long int, 998244353> ans = 0;
    for (long long int i = 1; i <= m; i++) {
      ans += (ModularArithmetic<long long int, 998244353>(mu[i]) * compute(i));
      {};
    }
    cout << ans << "\n";
  }
  int main() {
    freopen("err.txt", "w", stderr);
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    solve();
    return 0;
  }
  