#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 > 1e8) {
      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;
}

### Prompt

In cpp, your task is to solve the following problem:

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.

### Response

```cpp
#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 > 1e8) {
      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;
}

```