#include <bits/stdc++.h>
using namespace std;
template <typename T, typename U>
bool ckmin(T &a, const U &b) {
  return b < a ? a = b, true : false;
}
template <typename T, typename U>
bool ckmax(T &a, const U &b) {
  return b > a ? a = b, true : false;
}
const int N = 1e5 + 5;
const long long MOD = 998244353;
int n, m;
vector<int> mobius, lpf;
vector<array<int, 2>> ranges;
void least_prime_factor() {
  for (int i = 2; i < N; i++)
    if (!lpf[i])
      for (int j = i; j < N; j += i)
        if (!lpf[j]) lpf[j] = i;
}
void Mobius() {
  for (int i = 1; i < N; i++) {
    if (i == 1)
      mobius[i] = 1;
    else {
      if (lpf[i / lpf[i]] == lpf[i])
        mobius[i] = 0;
      else
        mobius[i] = -1 * mobius[i / lpf[i]];
    }
  }
}
long long solve(vector<array<int, 2>> &v, int sum) {
  vector<long long> cur(sum + 1, 0), nxt(sum + 1, 0);
  for (int i = v[0][0]; i <= v[0][1]; ++i) cur[i] = 1;
  for (int j = 1; j < n; ++j) {
    vector<long long> pc(sum + 2, 0);
    for (int i = 0; i < sum + 1; ++i) {
      pc[i + 1] = pc[i] + cur[i];
      pc[i + 1] %= MOD;
    }
    auto first = [&](int l, int r) -> long long {
      ckmax(l, 0);
      ckmax(r, 0);
      ckmin(l, sum);
      ckmin(r, sum);
      return pc[r + 1] - pc[l] + (pc[l] > pc[r + 1]) * MOD;
    };
    for (int i = 0; i <= sum; ++i) {
      int l = i - v[j][1], r = i - v[j][0];
      nxt[i] = first(l, r);
    }
    cur.swap(nxt);
    nxt.clear();
    pc.clear();
    nxt.assign(sum + 1, 0);
  }
  long long res = 0;
  for (auto i : cur) res += i;
  return res % MOD;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> m;
  ranges.assign(n, array<int, 2>());
  for (int i = 0; i < n; ++i) {
    cin >> ranges[i][0] >> ranges[i][1];
  }
  long long res = 0;
  lpf.assign(N, 0);
  least_prime_factor();
  mobius.assign(N, 0);
  Mobius();
  for (int g = 1; g <= m / n; ++g) {
    int cur_m = m / g;
    vector<array<int, 2>> cur_ranges = ranges;
    for (auto &i : cur_ranges) {
      i[0] = (i[0] - 1) / g + 1;
      i[1] /= g;
      if (i[1] < i[0]) goto nxt;
    }
    res += mobius[g] * solve(cur_ranges, cur_m);
    res %= MOD;
  nxt:;
  }
  cout << ((res % MOD) + MOD) % MOD;
  return 0;
}

### Prompt

Please create a solution in cpp to 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;
template <typename T, typename U>
bool ckmin(T &a, const U &b) {
  return b < a ? a = b, true : false;
}
template <typename T, typename U>
bool ckmax(T &a, const U &b) {
  return b > a ? a = b, true : false;
}
const int N = 1e5 + 5;
const long long MOD = 998244353;
int n, m;
vector<int> mobius, lpf;
vector<array<int, 2>> ranges;
void least_prime_factor() {
  for (int i = 2; i < N; i++)
    if (!lpf[i])
      for (int j = i; j < N; j += i)
        if (!lpf[j]) lpf[j] = i;
}
void Mobius() {
  for (int i = 1; i < N; i++) {
    if (i == 1)
      mobius[i] = 1;
    else {
      if (lpf[i / lpf[i]] == lpf[i])
        mobius[i] = 0;
      else
        mobius[i] = -1 * mobius[i / lpf[i]];
    }
  }
}
long long solve(vector<array<int, 2>> &v, int sum) {
  vector<long long> cur(sum + 1, 0), nxt(sum + 1, 0);
  for (int i = v[0][0]; i <= v[0][1]; ++i) cur[i] = 1;
  for (int j = 1; j < n; ++j) {
    vector<long long> pc(sum + 2, 0);
    for (int i = 0; i < sum + 1; ++i) {
      pc[i + 1] = pc[i] + cur[i];
      pc[i + 1] %= MOD;
    }
    auto first = [&](int l, int r) -> long long {
      ckmax(l, 0);
      ckmax(r, 0);
      ckmin(l, sum);
      ckmin(r, sum);
      return pc[r + 1] - pc[l] + (pc[l] > pc[r + 1]) * MOD;
    };
    for (int i = 0; i <= sum; ++i) {
      int l = i - v[j][1], r = i - v[j][0];
      nxt[i] = first(l, r);
    }
    cur.swap(nxt);
    nxt.clear();
    pc.clear();
    nxt.assign(sum + 1, 0);
  }
  long long res = 0;
  for (auto i : cur) res += i;
  return res % MOD;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> m;
  ranges.assign(n, array<int, 2>());
  for (int i = 0; i < n; ++i) {
    cin >> ranges[i][0] >> ranges[i][1];
  }
  long long res = 0;
  lpf.assign(N, 0);
  least_prime_factor();
  mobius.assign(N, 0);
  Mobius();
  for (int g = 1; g <= m / n; ++g) {
    int cur_m = m / g;
    vector<array<int, 2>> cur_ranges = ranges;
    for (auto &i : cur_ranges) {
      i[0] = (i[0] - 1) / g + 1;
      i[1] /= g;
      if (i[1] < i[0]) goto nxt;
    }
    res += mobius[g] * solve(cur_ranges, cur_m);
    res %= MOD;
  nxt:;
  }
  cout << ((res % MOD) + MOD) % MOD;
  return 0;
}

```