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:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Sandip Jana
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        private int MAX = 1_00_001;
        private int[] factors;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            sieve();

            // TODO build next reachable index
            int n = in.readInt(), q = in.readInt();
            int a[] = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = in.readInt();

            int maxSeen[] = new int[MAX];
            Arrays.fill(maxSeen, n);
            int reach[] = new int[n];
            Arrays.fill(reach, n);
            int nextPossible = n;
            for (int i = n - 1; i >= 0; i--) {
                ArrayList<Integer> factors = getFactors(a[i]);

                for (int x : factors)
                    nextPossible = Math.min(nextPossible, maxSeen[x]);

                reach[i] = nextPossible;
                for (int x : factors) maxSeen[x] = i;
            }

            // TODO apply binary lifting
            int log = 18;
            int binaryLift[][] = new int[n][log];
            for (int i = 0; i < n; i++)
                binaryLift[i][0] = reach[i];

            for (int j = 1; j < log; j++) {
                for (int i = 0; i < n; i++) {
                    if (binaryLift[i][j - 1] == n)
                        binaryLift[i][j] = n;
                    else
                        binaryLift[i][j] = binaryLift[binaryLift[i][j - 1]][j - 1];
                }
            }

            // TODO answer each query optimally
            for (int qq = 0; qq < q; qq++) {
                int l = in.readInt() - 1;
                int r = in.readInt() - 1;
                int cuts = 0;
                for (int j = log - 1; j >= 0; j--) {
                    if (binaryLift[l][j] <= r) {
                        cuts += 1 << j;
                        l = binaryLift[l][j];
                    }
                }
                out.println(cuts + 1);
            }
        }

        private ArrayList<Integer> getFactors(int x) {
            ArrayList<Integer> ret = new ArrayList<>();
            while (x > 1) {
                ret.add(factors[x]);
                int factor = factors[x];
                while (x % factor == 0) {
                    x /= factor;
                }
            }
            return ret;
        }

        private void sieve() {
            factors = new int[MAX];
            for (int i = 2; i < MAX; i++) {
                if (factors[i] == 0) {
                    for (int j = i; j < MAX; j += i)
                        factors[j] = i;
                }
            }
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}