#include <bits/stdc++.h>
using namespace std;
template <class T>
void REV(T *a, int n) {
  reverse(a + 1, a + 1 + n);
}
template <class T>
void SRT(T *a, int n) {
  sort(a + 1, a + 1 + n);
}
template <class T>
int UNI(T *a, int n) {
  sort(a + 1, a + 1 + n);
  return unique(a + 1, a + 1 + n) - (a + 1);
}
template <class T>
int POS(T *a, int n, T v) {
  return lower_bound(a + 1, a + 1 + n, v) - a;
}
template <class T>
int fisrtGe(T *a, int n, T v) {
  return lower_bound(a + 1, a + 1 + n, v) - a;
}
template <class T>
int lastLe(T *a, int n, T v) {
  return upper_bound(a + 1, a + 1 + n, v) - a - 1;
}
template <class T>
void _RD(T &x) {
  cin >> x;
}
void _RD(int &x) { scanf("%d", &x); }
void _RD(unsigned int &x) { scanf("%u", &x); }
void _RD(long long &x) { scanf("%lld", &x); }
void _RD(unsigned long long &x) { scanf("%llu", &x); }
void _RD(double &x) { scanf("%lf", &x); }
void _RD(char &x) { scanf(" %c", &x); }
void _RD(char *x) { scanf("%s", x + 1); }
template <class T, class U>
void _RD(pair<T, U> &x) {
  _RD(x.first);
  _RD(x.second);
}
void RD() {}
template <class T, class... U>
void RD(T &head, U &...tail) {
  _RD(head);
  RD(tail...);
}
template <class T>
void RDN(T *a, int n) {
  for (int i = 1; i <= n; ++i) _RD(a[i]);
}
template <class T>
void _WT(const T &x) {
  cout << x;
}
void _WT(const int &x) { printf("%d", x); }
void _WT(const unsigned int &x) { printf("%u", x); }
void _WT(const long long &x) { printf("%lld", x); }
void _WT(const unsigned long long &x) { printf("%llu", x); }
void _WT(const double &x) { printf("%.12f", x); }
void _WT(const char &x) { putchar(x); }
void _WT(const char *x) { printf("%s", x + 1); }
template <class T, class U>
void _WT(const pair<T, U> &x) {
  _WT(x.first);
  putchar(' ');
  _WT(x.second);
}
void WT() {}
template <class T, class... U>
void WT(const T &head, const U &...tail) {
  _WT(head);
  putchar(sizeof...(tail) ? ' ' : '\n');
  WT(tail...);
}
template <class T>
void WTN(T *a, int n) {
  for (int i = 1; i <= n; ++i) {
    _WT(a[i]);
    putchar(" \n"[i == n]);
  }
}
template <class T>
void WTV(const vector<T> &x, bool ln = false) {
  WT(x.size());
  for (auto i = x.begin(); i != x.end(); ++i) {
    _WT(*i);
    putchar(ln ? '\n' : ' ');
  }
  if (!ln) putchar('\n');
}
template <typename T>
void cmin(T &x, T y) {
  if (y < x) x = y;
}
template <typename T>
void cmax(T &x, T y) {
  if (y > x) x = y;
}
unsigned int rnd_seed = chrono::duration_cast<chrono::nanoseconds>(
                            chrono::steady_clock::now().time_since_epoch())
                            .count();
mt19937 rnd(rnd_seed);
const int INF = 0x3F3F3F3F;
const long long LINF = 0x3F3F3F3F3F3F3F3FLL;
int MOD = 998244353;
struct ModularIntegers {
  int num;
  ModularIntegers() { num = 0; }
  template <typename T>
  ModularIntegers(const T &x) {
    long long tmp = x;
    if (tmp >= MOD) {
      if (tmp < (MOD << 1))
        tmp -= MOD;
      else
        tmp %= MOD;
    } else if (tmp < 0) {
      if (tmp >= -MOD)
        tmp += MOD;
      else if (tmp %= MOD)
        tmp += MOD;
    }
    num = tmp;
  }
  friend ModularIntegers operator+(const ModularIntegers &x,
                                   const ModularIntegers &y) {
    return x.num + y.num;
  }
  friend ModularIntegers operator-(const ModularIntegers &x,
                                   const ModularIntegers &y) {
    return x.num - y.num;
  }
  friend ModularIntegers operator*(const ModularIntegers &x,
                                   const ModularIntegers &y) {
    return x.num * y.num;
  }
  friend ModularIntegers operator/(const ModularIntegers &x,
                                   const ModularIntegers &y) {
    return x * y.inv();
  }
  friend bool operator==(const ModularIntegers &x, const ModularIntegers &y) {
    return x.num == y.num;
  }
  friend bool operator!=(const ModularIntegers &x, const ModularIntegers &y) {
    return x.num != y.num;
  }
  ModularIntegers operator+() { return +this->num; }
  ModularIntegers operator-() { return -this->num; }
  ModularIntegers &operator+=(const ModularIntegers &x) {
    if ((this->num += x.num) >= MOD) this->num -= MOD;
    return *this;
  }
  ModularIntegers &operator-=(const ModularIntegers &x) {
    if ((this->num -= x.num) < 0) this->num += MOD;
    return *this;
  }
  ModularIntegers &operator*=(const ModularIntegers &x) {
    this->num = 1LL * this->num * x.num % MOD;
    return *this;
  }
  ModularIntegers &operator/=(const ModularIntegers &x) {
    this->num = ((*this) * x.inv()).num;
    return *this;
  }
  ModularIntegers pow(long long x) const {
    ModularIntegers res(1), cur(this->num);
    for (; x; cur *= cur, x >>= 1)
      if (x & 1) res *= cur;
    return res;
  }
  ModularIntegers inv() const { return pow(MOD - 2); }
  operator int() { return num; }
  operator unsigned int() { return num; }
  operator long long() { return num; }
  operator unsigned long long() { return num; }
};
void _RD(ModularIntegers &x) { scanf("%d", &x.num); }
void _WT(const ModularIntegers &x) { printf("%d", x.num); }
int n;
ModularIntegers tag[4000005];
void purin_solve() {
  RD(n, MOD);
  ModularIntegers pfi = 0;
  ModularIntegers ptag = 0;
  ModularIntegers ans = 0;
  for (int i = 1; i <= n; ++i) {
    ptag += tag[i];
    ModularIntegers fi = ptag + pfi;
    if (i == 1) fi = 1;
    for (int z = 2;; ++z) {
      int L = z * i;
      if (L > n) break;
      int R = min(n + 1, z * (i + 1));
      tag[L] += fi;
      tag[R] -= fi;
    }
    pfi += fi;
    ans = fi;
  }
  WT(ans);
}
int main() {
  cout << fixed << setprecision(12);
  cerr << fixed << setprecision(12);
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  int t = 1;
  while (t--) purin_solve();
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

Note that the memory limit in this problem is lower than in others.

You have a vertical strip with n cells, numbered consecutively from 1 to n from top to bottom.

You also have a token that is initially placed in cell n. You will move the token up until it arrives at cell 1.

Let the token be in cell x > 1 at some moment. One shift of the token can have either of the following kinds: 

  * Subtraction: you choose an integer y between 1 and x-1, inclusive, and move the token from cell x to cell x - y. 
  * Floored division: you choose an integer z between 2 and x, inclusive, and move the token from cell x to cell ⌊ x/z ⌋ (x divided by z rounded down). 



Find the number of ways to move the token from cell n to cell 1 using one or more shifts, and print it modulo m. Note that if there are several ways to move the token from one cell to another in one shift, all these ways are considered distinct (check example explanation for a better understanding).

Input

The only line contains two integers n and m (2 ≤ n ≤ 4 ⋅ 10^6; 10^8 < m < 10^9; m is a prime number) — the length of the strip and the modulo.

Output

Print the number of ways to move the token from cell n to cell 1, modulo m.

Examples

Input


3 998244353


Output


5


Input


5 998244353


Output


25


Input


42 998244353


Output


793019428


Input


787788 100000007


Output


94810539

Note

In the first test, there are three ways to move the token from cell 3 to cell 1 in one shift: using subtraction of y = 2, or using division by z = 2 or z = 3.

There are also two ways to move the token from cell 3 to cell 1 via cell 2: first subtract y = 1, and then either subtract y = 1 again or divide by z = 2.

Therefore, there are five ways in total.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <class T>
void REV(T *a, int n) {
  reverse(a + 1, a + 1 + n);
}
template <class T>
void SRT(T *a, int n) {
  sort(a + 1, a + 1 + n);
}
template <class T>
int UNI(T *a, int n) {
  sort(a + 1, a + 1 + n);
  return unique(a + 1, a + 1 + n) - (a + 1);
}
template <class T>
int POS(T *a, int n, T v) {
  return lower_bound(a + 1, a + 1 + n, v) - a;
}
template <class T>
int fisrtGe(T *a, int n, T v) {
  return lower_bound(a + 1, a + 1 + n, v) - a;
}
template <class T>
int lastLe(T *a, int n, T v) {
  return upper_bound(a + 1, a + 1 + n, v) - a - 1;
}
template <class T>
void _RD(T &x) {
  cin >> x;
}
void _RD(int &x) { scanf("%d", &x); }
void _RD(unsigned int &x) { scanf("%u", &x); }
void _RD(long long &x) { scanf("%lld", &x); }
void _RD(unsigned long long &x) { scanf("%llu", &x); }
void _RD(double &x) { scanf("%lf", &x); }
void _RD(char &x) { scanf(" %c", &x); }
void _RD(char *x) { scanf("%s", x + 1); }
template <class T, class U>
void _RD(pair<T, U> &x) {
  _RD(x.first);
  _RD(x.second);
}
void RD() {}
template <class T, class... U>
void RD(T &head, U &...tail) {
  _RD(head);
  RD(tail...);
}
template <class T>
void RDN(T *a, int n) {
  for (int i = 1; i <= n; ++i) _RD(a[i]);
}
template <class T>
void _WT(const T &x) {
  cout << x;
}
void _WT(const int &x) { printf("%d", x); }
void _WT(const unsigned int &x) { printf("%u", x); }
void _WT(const long long &x) { printf("%lld", x); }
void _WT(const unsigned long long &x) { printf("%llu", x); }
void _WT(const double &x) { printf("%.12f", x); }
void _WT(const char &x) { putchar(x); }
void _WT(const char *x) { printf("%s", x + 1); }
template <class T, class U>
void _WT(const pair<T, U> &x) {
  _WT(x.first);
  putchar(' ');
  _WT(x.second);
}
void WT() {}
template <class T, class... U>
void WT(const T &head, const U &...tail) {
  _WT(head);
  putchar(sizeof...(tail) ? ' ' : '\n');
  WT(tail...);
}
template <class T>
void WTN(T *a, int n) {
  for (int i = 1; i <= n; ++i) {
    _WT(a[i]);
    putchar(" \n"[i == n]);
  }
}
template <class T>
void WTV(const vector<T> &x, bool ln = false) {
  WT(x.size());
  for (auto i = x.begin(); i != x.end(); ++i) {
    _WT(*i);
    putchar(ln ? '\n' : ' ');
  }
  if (!ln) putchar('\n');
}
template <typename T>
void cmin(T &x, T y) {
  if (y < x) x = y;
}
template <typename T>
void cmax(T &x, T y) {
  if (y > x) x = y;
}
unsigned int rnd_seed = chrono::duration_cast<chrono::nanoseconds>(
                            chrono::steady_clock::now().time_since_epoch())
                            .count();
mt19937 rnd(rnd_seed);
const int INF = 0x3F3F3F3F;
const long long LINF = 0x3F3F3F3F3F3F3F3FLL;
int MOD = 998244353;
struct ModularIntegers {
  int num;
  ModularIntegers() { num = 0; }
  template <typename T>
  ModularIntegers(const T &x) {
    long long tmp = x;
    if (tmp >= MOD) {
      if (tmp < (MOD << 1))
        tmp -= MOD;
      else
        tmp %= MOD;
    } else if (tmp < 0) {
      if (tmp >= -MOD)
        tmp += MOD;
      else if (tmp %= MOD)
        tmp += MOD;
    }
    num = tmp;
  }
  friend ModularIntegers operator+(const ModularIntegers &x,
                                   const ModularIntegers &y) {
    return x.num + y.num;
  }
  friend ModularIntegers operator-(const ModularIntegers &x,
                                   const ModularIntegers &y) {
    return x.num - y.num;
  }
  friend ModularIntegers operator*(const ModularIntegers &x,
                                   const ModularIntegers &y) {
    return x.num * y.num;
  }
  friend ModularIntegers operator/(const ModularIntegers &x,
                                   const ModularIntegers &y) {
    return x * y.inv();
  }
  friend bool operator==(const ModularIntegers &x, const ModularIntegers &y) {
    return x.num == y.num;
  }
  friend bool operator!=(const ModularIntegers &x, const ModularIntegers &y) {
    return x.num != y.num;
  }
  ModularIntegers operator+() { return +this->num; }
  ModularIntegers operator-() { return -this->num; }
  ModularIntegers &operator+=(const ModularIntegers &x) {
    if ((this->num += x.num) >= MOD) this->num -= MOD;
    return *this;
  }
  ModularIntegers &operator-=(const ModularIntegers &x) {
    if ((this->num -= x.num) < 0) this->num += MOD;
    return *this;
  }
  ModularIntegers &operator*=(const ModularIntegers &x) {
    this->num = 1LL * this->num * x.num % MOD;
    return *this;
  }
  ModularIntegers &operator/=(const ModularIntegers &x) {
    this->num = ((*this) * x.inv()).num;
    return *this;
  }
  ModularIntegers pow(long long x) const {
    ModularIntegers res(1), cur(this->num);
    for (; x; cur *= cur, x >>= 1)
      if (x & 1) res *= cur;
    return res;
  }
  ModularIntegers inv() const { return pow(MOD - 2); }
  operator int() { return num; }
  operator unsigned int() { return num; }
  operator long long() { return num; }
  operator unsigned long long() { return num; }
};
void _RD(ModularIntegers &x) { scanf("%d", &x.num); }
void _WT(const ModularIntegers &x) { printf("%d", x.num); }
int n;
ModularIntegers tag[4000005];
void purin_solve() {
  RD(n, MOD);
  ModularIntegers pfi = 0;
  ModularIntegers ptag = 0;
  ModularIntegers ans = 0;
  for (int i = 1; i <= n; ++i) {
    ptag += tag[i];
    ModularIntegers fi = ptag + pfi;
    if (i == 1) fi = 1;
    for (int z = 2;; ++z) {
      int L = z * i;
      if (L > n) break;
      int R = min(n + 1, z * (i + 1));
      tag[L] += fi;
      tag[R] -= fi;
    }
    pfi += fi;
    ans = fi;
  }
  WT(ans);
}
int main() {
  cout << fixed << setprecision(12);
  cerr << fixed << setprecision(12);
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  int t = 1;
  while (t--) purin_solve();
  return 0;
}

```