Problem: We call an array b_1, b_2, …, b_m good, if there exist two indices i < j such that b_i ⋅ b_j is a [perfect square](https://en.wikipedia.org/wiki/Square_number).

Given an array b_1, b_2, …, b_m, in one action you can perform one of the following: 

  * multiply any element b_i by any prime p; 
  * divide any element b_i by prime p, if b_i is divisible by p. 



Let f(b_1, b_2, …, b_m) be the minimum number of actions needed to make the array b good.

You are given an array of n integers a_1, a_2, …, a_n and q queries of the form l_i, r_i. For each query output f(a_{l_i}, a_{l_i + 1}, …, a_{r_i}).

Input

The first line contains two integers n and q (2 ≤ n ≤ 194 598, 1 ≤ q ≤ 1 049 658) — the length of the array and the number of queries.

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 5 032 107) — the elements of the array.

Each of the next q lines contains two integers l_i and r_i (1 ≤ l_i < r_i ≤ n) — the parameters of a query.

Output

Output q lines — the answers for each query in the order they are given in the input.

Example

Input

10 10
34 37 28 16 44 36 43 50 22 13
1 3
4 8
6 10
9 10
3 10
8 9
5 6
1 4
1 7
2 6


Output

2
0
1
3
0
1
1
1
0
0

Note

In the first query of the first sample you can multiply second number by 7 to get 259 and multiply the third one by 37 to get 1036. Then a_2 ⋅ a_3 = 268 324 = 518^2.

In the second query subarray is already good because a_4 ⋅ a_6 = 24^2.

In the third query you can divide 50 by 2 to get 25. Then a_6 ⋅ a_8 = 30^2.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
template <typename T>
inline T max(T a, T b) {
  return a > b ? a : b;
}
template <typename T>
inline T min(T a, T b) {
  return a < b ? a : b;
}
template <typename T>
inline T abs(T a) {
  return a > 0 ? a : -a;
}
template <typename T>
inline bool repr(T &a, T b) {
  return a < b ? a = b, 1 : 0;
}
template <typename T>
inline bool repl(T &a, T b) {
  return a > b ? a = b, 1 : 0;
}
template <typename T>
inline T gcd(T a, T b) {
  T t;
  if (a < b) {
    while (a) {
      t = a;
      a = b % a;
      b = t;
    }
    return b;
  } else {
    while (b) {
      t = b;
      b = a % b;
      a = t;
    }
    return a;
  }
}
template <typename T>
inline T sqr(T x) {
  return x * x;
}
struct Cg {
  inline char operator()() { return getchar(); }
};
struct Cp {
  inline void operator()(char x) { putchar(x); }
};
inline bool IS(char x) { return x == 10 || x == 13 || x == ' '; }
template <typename T>
struct Fr {
  T P;
  inline Fr &operator,(int &x) {
    x = 0;
    unsigned char t = P();
    while ((t < '0' || t > '9') && t != '-') t = P();
    bool f = 0;
    if (t == '-') t = P(), f = 1;
    x = t - '0';
    for (t = P(); t >= '0' && t <= '9'; t = P()) x = x * 10 + t - '0';
    if (f) x = -x;
    return *this;
  }
  inline operator int() {
    int x;
    *this, x;
    return x;
  }
  inline Fr &operator,(long long &x) {
    x = 0;
    unsigned char t = P();
    while ((t < '0' || t > '9') && t != '-') t = P();
    bool f = 0;
    if (t == '-') t = P(), f = 1;
    x = t - '0';
    for (t = P(); t >= '0' && t <= '9'; t = P()) x = x * 10 + t - '0';
    if (f) x = -x;
    return *this;
  }
  inline operator long long() {
    long long x;
    *this, x;
    return x;
  }
  inline Fr &operator,(char &x) {
    for (x = P(); IS(x); x = P())
      ;
    return *this;
  }
  inline operator char() {
    char x;
    *this, x;
    return x;
  }
  inline Fr &operator,(char *x) {
    char t = P();
    for (; IS(t); t = P())
      ;
    if (~t) {
      for (; !IS(t) && ~t; t = P()) *x++ = t;
    }
    *x++ = 0;
    return *this;
  }
  inline Fr &operator,(double &x) {
    x = 0;
    unsigned char t = P();
    while ((t < '0' || t > '9') && t != '-') t = P();
    bool f = 0;
    if (t == '-') t = P(), f = 1;
    x = t - '0';
    for (t = P(); t >= '0' && t <= '9'; t = P()) x = x * 10 + t - '0';
    if (t == '.') {
      double u = 0.1;
      for (t = P(); t >= '0' && t <= '9'; t = P(), u *= 0.1) x += u * (t - '0');
    }
    if (f) x = -x;
    return *this;
  }
  inline operator double() {
    double x;
    *this, x;
    return x;
  }
  inline Fr &operator,(long double &x) {
    x = 0;
    unsigned char t = P();
    while ((t < '0' || t > '9') && t != '-') t = P();
    bool f = 0;
    if (t == '-') t = P(), f = 1;
    x = t - '0';
    for (t = P(); t >= '0' && t <= '9'; t = P()) x = x * 10 + t - '0';
    if (t == '.') {
      double u = 0.1;
      for (t = P(); t >= '0' && t <= '9'; t = P(), u *= 0.1) x += u * (t - '0');
    }
    if (f) x = -x;
    return *this;
  }
  inline operator long double() {
    long double x;
    *this, x;
    return x;
  }
  inline Fr &operator,(unsigned int &x) {
    x = 0;
    unsigned char t = P();
    while (t < '0' || t > '9') t = P();
    x = t - '0';
    for (t = P(); t >= '0' && t <= '9'; t = P()) x = x * 10 + t - '0';
    return *this;
  }
  inline operator unsigned int() {
    unsigned int x;
    *this, x;
    return x;
  }
  inline Fr &operator,(unsigned long long &x) {
    x = 0;
    unsigned char t = P();
    while (t < '0' || t > '9') t = P();
    x = t - '0';
    for (t = P(); t >= '0' && t <= '9'; t = P()) x = x * 10 + t - '0';
    return *this;
  }
  inline operator unsigned long long() {
    unsigned long long x;
    *this, x;
    return x;
  }
};
Fr<Cg> in;
template <typename T>
struct Fw {
  T P;
  inline Fw &operator,(int x) {
    if (x) {
      if (x < 0) P('-'), x = -x;
      unsigned char s[10], c = 0;
      while (x) s[c++] = x % 10 + '0', x /= 10;
      while (c--) P(s[c]);
    } else
      P('0');
    return *this;
  }
  inline Fw &operator()(int x) {
    if (x) {
      if (x < 0) P('-'), x = -x;
      unsigned char s[10], c = 0;
      while (x) s[c++] = x % 10 + '0', x /= 10;
      while (c--) P(s[c]);
    } else
      P('0');
    return *this;
  }
  inline Fw &operator,(unsigned int x) {
    if (x) {
      unsigned char s[10], c = 0;
      while (x) s[c++] = x % 10 + '0', x /= 10;
      while (c--) P(s[c]);
    } else
      P('0');
    return *this;
  }
  inline Fw &operator()(unsigned int x) {
    if (x) {
      unsigned char s[10], c = 0;
      while (x) s[c++] = x % 10 + '0', x /= 10;
      while (c--) P(s[c]);
    } else
      P('0');
    return *this;
  }
  inline Fw &operator,(long long x) {
    if (x) {
      if (x < 0) P('-'), x = -x;
      unsigned char s[19], c = 0;
      while (x) s[c++] = x % 10 + '0', x /= 10;
      while (c--) P(s[c]);
    } else
      P('0');
    return *this;
  }
  inline Fw &operator()(long long x) {
    if (x) {
      if (x < 0) P('-'), x = -x;
      unsigned char s[19], c = 0;
      while (x) s[c++] = x % 10 + '0', x /= 10;
      while (c--) P(s[c]);
    } else
      P('0');
    return *this;
  }
  inline Fw &operator,(unsigned long long x) {
    if (x) {
      unsigned char s[20], c = 0;
      while (x) s[c++] = x % 10 + '0', x /= 10;
      while (c--) P(s[c]);
    } else
      P('0');
    return *this;
  }
  inline Fw &operator()(unsigned long long x) {
    if (x) {
      unsigned char s[20], c = 0;
      while (x) s[c++] = x % 10 + '0', x /= 10;
      while (c--) P(s[c]);
    } else
      P('0');
    return *this;
  }
  inline Fw &operator,(char x) {
    P(x);
    return *this;
  }
  inline Fw &operator()(char x) {
    P(x);
    return *this;
  }
  inline Fw &operator,(const char *x) {
    while (*x) P(*x++);
    return *this;
  }
  inline Fw &operator()(const char *x) {
    while (*x) P(*x++);
    return *this;
  }
  inline Fw &operator()(double x, int y) {
    if (y) {
      double t = 0.5;
      for (int i = y; i--;) t *= 0.1;
      if (x >= 0)
        x += t;
      else
        x -= t, P('-');
      *this, (long long)(abs(x));
      P('.');
      if (x < 0) x = -x;
      while (y--) {
        x *= 10;
        x -= floor(x * 0.1) * 10;
        P(((int)x) % 10 + '0');
      }
    } else if (x >= 0)
      *this, (long long)(x + 0.5);
    else
      *this, (long long)(x - 0.5);
    ;
    return *this;
  }
  inline Fw &operator()(long double x, int y) {
    if (y) {
      double t = 0.5;
      for (int i = y; i--;) t *= 0.1;
      if (x >= 0)
        x += t;
      else
        x -= t, P('-');
      *this, (long long)(abs(x));
      P('.');
      if (x < 0) x = -x;
      while (y--) {
        x *= 10;
        x -= floor(x * 0.1) * 10;
        P(((int)x) % 10 + '0');
      }
    } else if (x >= 0)
      *this, (long long)(x + 0.5);
    else
      *this, (long long)(x - 0.5);
    ;
    return *this;
  }
};
Fw<Cp> out;
#pragma GCC target("popcnt")
const int N = 200007, M = 1050007, V = 5050007, inf = 0x3f3f3f3f;
std::vector<std::pair<int, int> > q[N];
int n, m, pm, s[N], ans[M], p[V / 10], lo[V], lp[V], f[7], fc, fs[133], g[V][8],
    ua[15];
char mu[V];
int main() {
  for (int i = 2, iend = V - 1; i <= iend; i++) {
    if (!lo[i]) p[pm++] = i, lo[i] = i, mu[i] = -1, lp[i] = i;
    for (int j = 0; i * p[j] < V; j++) {
      lp[i * p[j]] = p[j];
      if (lo[i] % p[j] == 0)
        lo[i * p[j]] = lo[i] / p[j];
      else
        lo[i * p[j]] = lo[i] * p[j];
      if (i % p[j] == 0) {
        break;
      }
      mu[i * p[j]] = -mu[i];
    }
  }
  lo[1] = 1, lp[1] = 1, mu[1] = 1;
  in, n, m;
  for (int i = 1, iend = n; i <= iend; i++) in, s[i];
  for (int i = 1, iend = m; i <= iend; i++) {
    int l, r;
    in, l, r;
    q[r].push_back(std::make_pair(l, i));
  }
  for (int i = 1, iend = n; i <= iend; i++) {
    int t = lo[s[i]];
    fc = 0;
    while (t > 1) f[fc++] = lp[t], t /= lp[t];
    fs[0] = 1;
    for (int j = 0, jend = fc; j < jend; j++) fs[1 << j] = f[j];
    for (int j = 1, jend = (1 << fc) - 1; j <= jend; j++) {
      fs[j] = fs[j & (j - 1)] * fs[j & -j];
    }
    for (int j = 0, jend = 1 << fc; j < jend; j++) {
      int x = fs[j], y = fc - __builtin_popcount(j);
      for (int k = 0, kend = 8; k < kend; k++) repr(ua[k + y], g[x][k]);
      g[x][y] = i;
    }
    for (__typeof((q[i]).end()) j = (q[i]).begin(); j != (q[i]).end(); ++j) {
      for (int k = 0, kend = 15; k < kend; k++)
        if (ua[k] >= j->first) {
          ans[j->second] = k;
          break;
        }
    }
  }
  for (int i = 1, iend = m; i <= iend; i++) out, ans[i], '\n';
}