Problem: This time Baby Ehab will only cut and not stick. He starts with a piece of paper with an array a of length n written on it, and then he does the following:

  * he picks a range (l, r) and cuts the subsegment a_l, a_{l + 1}, …, a_r out, removing the rest of the array. 
  * he then cuts this range into multiple subranges. 
  * to add a number theory spice to it, he requires that the elements of every subrange must have their product equal to their [least common multiple (LCM)](https://en.wikipedia.org/wiki/Least_common_multiple). 



Formally, he partitions the elements of a_l, a_{l + 1}, …, a_r into contiguous subarrays such that the product of every subarray is equal to its LCM. Now, for q independent ranges (l, r), tell Baby Ehab the minimum number of subarrays he needs.

Input

The first line contains 2 integers n and q (1 ≤ n,q ≤ 10^5) — the length of the array a and the number of queries.

The next line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^5) — the elements of the array a.

Each of the next q lines contains 2 integers l and r (1 ≤ l ≤ r ≤ n) — the endpoints of this query's interval.

Output

For each query, print its answer on a new line.

Example

Input


6 3
2 3 10 7 5 14
1 6
2 4
3 5


Output


3
1
2

Note

The first query asks about the whole array. You can partition it into [2], [3,10,7], and [5,14]. The first subrange has product and LCM equal to 2. The second has product and LCM equal to 210. And the third has product and LCM equal to 70. Another possible partitioning is [2,3], [10,7], and [5,14].

The second query asks about the range (2,4). Its product is equal to its LCM, so you don't need to partition it further.

The last query asks about the range (3,5). You can partition it into [10,7] and [5].

Solution (in JAVA):

Solution:
//package codeforces.contest_717d2;

import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashSet;
import java.util.List;
import java.util.Objects;
import java.util.Random;
import java.util.Set;
import java.util.StringTokenizer;

public class D {

  static MyScanner scanner = new MyScanner();
  static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
  static final int MOD = 1000000007;
  static final boolean oj = System.getProperty("ONLINE_JUDGE") != null;
  static final int[][] d4 = new int[][]{{-1, 0}, {0, -1}, {1, 0}, {0, 1}};
  static final int[][] d8 = new int[][]{{-1, -1}, {-1, 0}, {-1, 1}, {0, -1}, {0, 1}, {1, -1}, {1, 0}, {1, 1}};
  static final int N = 0;

  static int primes[]=new int[]{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
      73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167,
      173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269,
      271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379,
      383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487,
      491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607,
      613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727,
      733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853,
      857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977,
      983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087,
      1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201,
      1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303,
      1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447,
      1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607,
      1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721,
      1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847,
      1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973,
      1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081,
      2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203,
      2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309,
      2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411,
      2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549,
      2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677,
      2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767,
      2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887,
      2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019,
      3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167,
      3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299,
      3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373,
      3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517,
      3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617,
      3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739,
      3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889,
      3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021,
      4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159,
      4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297,
      4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463,
      4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621,
      4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759,
      4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931,
      4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999};

  private static List<Integer> get(int a) {
    List<Integer> ps = new ArrayList<>();
    for(int prime : primes) {
      if(a%prime == 0) {
        while(a%prime == 0) a /= prime;
        ps.add(prime);
      }
    }
    if(a != 1) ps.add(a);
    return ps;
  }

  public static void main(String[] args) {
    int tc = 1;
    for(int t=0; t<tc; t++) {
      int n = scanner.nextInt();
      int q = scanner.nextInt();
      int[] a = getIntArr(n);
      List<Integer>[] pss = new List[n];
      for(int i=0; i<n; i++) {
        pss[i] = get(a[i]);
      }

      int j = 0;
      int[][] f = new int[n+1][20];
      Set<Integer> ks = new HashSet<>();
      for(int i=0; i<n; i++) {
        for(int v : pss[i]) {
          while(ks.contains(v)) {
            f[j][0] = i;
            for(int v1 : pss[j]) ks.remove(v1);
            j++;
          }
          ks.add(v);
        }
      }
      for(; j<n+1; j++) f[j][0] = n;
//      for(int i=0; i<=n; i++) out.print(f[i][0] + " ");
//      out.println();
      for(int i=1; i<20; i++) {
        for(j=0; j<=n; j++) {
          f[j][i] = f[f[j][i-1]][i-1];
        }
      }

      for(j=0; j<q; j++) {
        int l = scanner.nextInt()-1, r = scanner.nextInt()-1, res = 0;
        for(int i=19; i>=0; i--) {
          if(f[l][i] > r) continue;
          res += (1<<i);
          l = f[l][i];
        }
        out.println(res+1);
      }
    }
    out.close();
  }

  private static int[] getIntArr(int n) {
    int[] a = new int[n];
    for(int i=0; i<n; i++) {
      a[i] = scanner.nextInt();
    }
    return a;
  }

  private static long[] getLongArr(int n) {
    long[] a = new long[n];
    for(int i=0; i<n; i++) {
      a[i] = scanner.nextLong();
    }
    return a;
  }

  public static void print(Object o) {
    if(!oj) {
      out.println(o);
    }
  }

  //Find the GCD of two numbers
  public static long gcd(long a, long b) {
    if (a < b) return gcd(b,a);
    if (b == 0)
      return a;
    else
      return gcd(b,a%b);
  }

  private static long[] fac = new long[N+1];
  private static long[] invfac = new long[N+1];

  private static long fac(int n){
    if(n == 0) return fac[0] = 1;
    else if(fac[n] > 0) return fac[n];
    else return fac[n] = n * fac(n-1) % MOD;
  }

  private static long invfac(int n){
    if(invfac[n] > 0) return invfac[n];
    else return invfac[n] = inv(fac[n]);
  }

  private static long choose(int n, int k){
    return fac(n) * invfac(k) % MOD * invfac(n-k) % MOD;
  }

  private static long inv(long a){
    return (gcdex(a, MOD).key + MOD) % MOD;
  }

  private static Pair<Long, Long> gcdex(long a, long b){
    if(b > a) return gcdex(b, a).invert();
    else if(b == 0) return new Pair<>(1L, 0L);
    else{
      Pair<Long, Long> p = gcdex(b, a % b);
      return new Pair<>(p.key, p.key - p.value*(a/b));
    }
  }

  //Fast exponentiation (x^y mod m)
  public static long power(long x, long y, long m) {
    if (y < 0) return 0L;
    long ans = 1;
    x %= m;
    while (y > 0) {
      if(y % 2 == 1)
        ans = (ans * x) % m;
      y /= 2;
      x = (x * x) % m;
    }
    return ans;
  }

  public static int[] shuffle(int[] array) {
    Random rgen = new Random();
    for (int i = 0; i < array.length; i++) {
      int randomPosition = rgen.nextInt(array.length);
      int temp = array[i];
      array[i] = array[randomPosition];
      array[randomPosition] = temp;
    }
    return array;
  }

  public static long[] shuffle(long[] array) {
    Random rgen = new Random();
    for (int i = 0; i < array.length; i++) {
      int randomPosition = rgen.nextInt(array.length);
      long temp = array[i];
      array[i] = array[randomPosition];
      array[randomPosition] = temp;
    }
    return array;
  }

  public static int[][] shuffle(int[][] array) {
    Random rgen = new Random();
    for (int i = 0; i < array.length; i++) {
      int randomPosition = rgen.nextInt(array.length);
      int[] temp = array[i];
      array[i] = array[randomPosition];
      array[randomPosition] = temp;
    }
    return array;
  }

  public static int[][] sort(int[][] array) {
    //Sort an array (immune to quicksort TLE)

    Arrays.sort(array, new Comparator<int[]>() {
      @Override
      public int compare(int[] a, int[] b) {
        return a[1]-b[1]; //ascending order
      }
    });
    return array;
  }

  public static long[][] sort(long[][] array) {
    //Sort an array (immune to quicksort TLE)
    Random rgen = new Random();
    for (int i = 0; i < array.length; i++) {
      int randomPosition = rgen.nextInt(array.length);
      long[] temp = array[i];
      array[i] = array[randomPosition];
      array[randomPosition] = temp;
    }
    Arrays.sort(array, new Comparator<long[]>() {
      @Override
      public int compare(long[] a, long[] b) {
        if (a[0] < b[0])
          return -1;
        else if (a[0] > b[0])
          return 1;
        else
          return 0;
      }
    });
    return array;
  }

  static class MyScanner {
    private BufferedReader br;
    private StringTokenizer st;

    MyScanner() {
      br = new BufferedReader(new InputStreamReader(System.in));
    }

    String next() {
      while (st == null || !st.hasMoreElements()) {
        try {
          st = new StringTokenizer(br.readLine());
        } catch (IOException e) {
          e.printStackTrace();
        }
      }
      return st.nextToken();
    }

    int nextInt() {
      return Integer.parseInt(next());
    }

    long nextLong() {
      return Long.parseLong(next());
    }

    double nextDouble() {
      return Double.parseDouble(next());
    }

    String nextLine(){
      String str = "";
      try {
        str = br.readLine();
      } catch (IOException e) {
        e.printStackTrace();
      }
      return str;
    }
  }

  static class Pair<K,V> {

    public K key;
    public V value;

    public Pair(K key, V value) {
      this.key = key;
      this.value = value;
    }

    @Override
    public String toString() {
      return key + ":" + value;
    }

    @Override
    public int hashCode() {
      return key.hashCode() * 13 + (value == null ? 0 : value.hashCode());
    }

    @Override
    public boolean equals(Object o) {
      if (this == o) return true;
      if (o instanceof Pair) {
        Pair pair = (Pair) o;
        return Objects.equals(key, pair.key) && Objects.equals(value, pair.value);
      }
      return false;
    }

    public Pair<V, K> invert() {
      return new Pair<>(value, key);
    }
  }

  static class Triple<A, B, C> {
    public A a;
    public B b;
    public C c;

    public Triple(A a, B b, C c) {
      this.a = a;
      this.b = b;
      this.c = c;
    }

    @Override
    public String toString() {
      return a + ":" + b + ":" + c;
    }

    @Override
    public int hashCode() {
      return (a == null ? 0 : a.hashCode()) * 13 + (b == null ? 0 : b.hashCode()) * 41 + (c == null ? 0 : c.hashCode());
    }

    @Override
    public boolean equals(Object o) {
      if (this == o) return true;
      if (o instanceof Triple) {
        Triple triple = (Triple) o;
        return Objects.equals(a, triple.a) && Objects.equals(b, triple.b) && Objects.equals(c, triple.c);
      }
      return false;
    }
  }
}