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 PYTHON3):

Solution:
import os
import sys
import time
from functools import lru_cache
from io import BytesIO, IOBase


def main():
    limit = 10 ** 5 + 1
    R = [0] * limit
    for i in range(2, limit):
        if not R[i]:
            for j in range(i * i, limit, i):
                if not R[j]:
                    R[j] = i

    @lru_cache(None)
    def get_divs(n):
        if n == 1:
            return tuple()
        s = set()
        while R[n]:
            s.add(R[n])
            n //= R[n]
        s.add(n)
        return s

    n, q = li_input()
    a = li_input()

    all_divs = {}
    p = [0] * n
    j = 0
    for i, aa in enumerate(a):
        while j < n:
            divs_j = get_divs(a[j])
            if any((div_j in all_divs for div_j in divs_j)):
                break
            for div_j in divs_j:
                if div_j in all_divs:
                    all_divs[div_j] += 1
                else:
                    all_divs[div_j] = 1
            j += 1

        p[i] = j
        divs_i = get_divs(a[i])
        for div_i in divs_i:
            all_divs[div_i] -= 1
            if not all_divs[div_i]:
                all_divs.pop(div_i)

    A = [p]
    need_to_continue = True
    while need_to_continue:
        need_to_continue = False
        A.append([n] * n)
        for i in range(n):
            if A[-2][i] != n:
                A[-1][i] = A[-2][A[-2][i]]
                if A[-1][i] != n:
                    need_to_continue = True

    out = []
    for qq in range(q):
        ans = 1
        l, r = li_input()
        l -= 1
        r -= 1

        for i in range(len(A) - 1, -1, -1):
            if A[i][l] <= r:
                ans += 1 << i
                l = A[i][l]

        out.append(ans)

    print("\n".join(map(str, out)))


############

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


def print(*args, **kwargs):
    """Prints the values to a stream, or to sys.stdout by default."""
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)


def input():
    return sys.stdin.readline().rstrip("\r\n")


def i_input():
    return int(input())


def l_input():
    return input().split()


def li_input():
    return list(map(int, l_input()))


def il_input():
    return list(map(int, l_input()))


# endregion

if __name__ == "__main__":
    TT = time.time()
    main()
    # print("\n", time.time() - TT)