There are several days left before the fiftieth birthday of a famous Berland's writer Berlbury. In this connection the local library decided to make an exposition of the works of this famous science-fiction writer. It was decided as well that it is necessary to include into the exposition only those books that were published during a particular time period. It is obvious that if the books differ much in size, the visitors will not like it. That was why the organizers came to the opinion, that the difference between the highest and the lowest books in the exposition should be not more than k millimeters.

The library has n volumes of books by Berlbury, arranged in chronological order of their appearance. The height of each book in millimeters is know, it is hi. As Berlbury is highly respected in the city, the organizers want to include into the exposition as many books as possible, and to find out what periods of his creative work they will manage to cover. You are asked to help the organizers cope with this hard task.

Input

The first line of the input data contains two integer numbers separated by a space n (1 ≤ n ≤ 105) and k (0 ≤ k ≤ 106) — the amount of books by Berlbury in the library, and the maximum allowed height difference between the lowest and the highest books. The second line contains n integer numbers separated by a space. Each number hi (1 ≤ hi ≤ 106) is the height of the i-th book in millimeters.

Output

In the first line of the output data print two numbers a and b (separate them by a space), where a is the maximum amount of books the organizers can include into the exposition, and b — the amount of the time periods, during which Berlbury published a books, and the height difference between the lowest and the highest among these books is not more than k milllimeters.

In each of the following b lines print two integer numbers separated by a space — indexes of the first and the last volumes from each of the required time periods of Berlbury's creative work.

Examples

Input

3 3
14 12 10


Output

2 2
1 2
2 3


Input

2 0
10 10


Output

2 1
1 2


Input

4 5
8 19 10 13


Output

2 1
3 4
"""
#If FastIO not needed, use this and don't forget to strip
#import sys, math
#input = sys.stdin.readline
"""

import os
import sys
from io import BytesIO, IOBase
import heapq as h 
from bisect import bisect_left, bisect_right
import time

from types import GeneratorType
BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0
 
    def __init__(self, file):
        import os
        self.os = os
        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 = self.os.read(self._fd, max(self.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 = self.os.read(self._fd, max(self.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:
            self.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")
 
 
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

from collections import defaultdict as dd, deque as dq, Counter as dc
import string
from math import sqrt

#start_time = time.time()

def getInts():
    return [int(s) for s in input().split()]

def getInt():
    return int(input())

def getStrs():
    return [s for s in input().split()]

def getStr():
    return input()

def listStr():
    return list(input())

def getMat(n):
    return [getInts() for _ in range(n)]

def isInt(s):
    return '0' <= s[0] <= '9'

MOD = 10**9 + 7 

class SortedList:
    def __init__(self, iterable=[], _load=200):
        """Initialize sorted list instance."""
        values = sorted(iterable)
        self._len = _len = len(values)
        self._load = _load
        self._lists = _lists = [values[i:i + _load] for i in range(0, _len, _load)]
        self._list_lens = [len(_list) for _list in _lists]
        self._mins = [_list[0] for _list in _lists]
        self._fen_tree = []
        self._rebuild = True
 
    def _fen_build(self):
        """Build a fenwick tree instance."""
        self._fen_tree[:] = self._list_lens
        _fen_tree = self._fen_tree
        for i in range(len(_fen_tree)):
            if i | i + 1 < len(_fen_tree):
                _fen_tree[i | i + 1] += _fen_tree[i]
        self._rebuild = False
 
    def _fen_update(self, index, value):
        """Update `fen_tree[index] += value`."""
        if not self._rebuild:
            _fen_tree = self._fen_tree
            while index < len(_fen_tree):
                _fen_tree[index] += value
                index |= index + 1
 
    def _fen_query(self, end):
        """Return `sum(_fen_tree[:end])`."""
        if self._rebuild:
            self._fen_build()
 
        _fen_tree = self._fen_tree
        x = 0
        while end:
            x += _fen_tree[end - 1]
            end &= end - 1
        return x
 
    def _fen_findkth(self, k):
        """Return a pair of (the largest `idx` such that `sum(_fen_tree[:idx]) <= k`, `k - sum(_fen_tree[:idx])`)."""
        _list_lens = self._list_lens
        if k < _list_lens[0]:
            return 0, k
        if k >= self._len - _list_lens[-1]:
            return len(_list_lens) - 1, k + _list_lens[-1] - self._len
        if self._rebuild:
            self._fen_build()
 
        _fen_tree = self._fen_tree
        idx = -1
        for d in reversed(range(len(_fen_tree).bit_length())):
            right_idx = idx + (1 << d)
            if right_idx < len(_fen_tree) and k >= _fen_tree[right_idx]:
                idx = right_idx
                k -= _fen_tree[idx]
        return idx + 1, k
 
    def _delete(self, pos, idx):
        """Delete value at the given `(pos, idx)`."""
        _lists = self._lists
        _mins = self._mins
        _list_lens = self._list_lens
 
        self._len -= 1
        self._fen_update(pos, -1)
        del _lists[pos][idx]
        _list_lens[pos] -= 1
 
        if _list_lens[pos]:
            _mins[pos] = _lists[pos][0]
        else:
            del _lists[pos]
            del _list_lens[pos]
            del _mins[pos]
            self._rebuild = True
 
    def _loc_left(self, value):
        """Return an index pair that corresponds to the first position of `value` in the sorted list."""
        if not self._len:
            return 0, 0
 
        _lists = self._lists
        _mins = self._mins
 
        lo, pos = -1, len(_lists) - 1
        while lo + 1 < pos:
            mi = (lo + pos) >> 1
            if value <= _mins[mi]:
                pos = mi
            else:
                lo = mi
 
        if pos and value <= _lists[pos - 1][-1]:
            pos -= 1
 
        _list = _lists[pos]
        lo, idx = -1, len(_list)
        while lo + 1 < idx:
            mi = (lo + idx) >> 1
            if value <= _list[mi]:
                idx = mi
            else:
                lo = mi
 
        return pos, idx
 
    def _loc_right(self, value):
        """Return an index pair that corresponds to the last position of `value` in the sorted list."""
        if not self._len:
            return 0, 0
 
        _lists = self._lists
        _mins = self._mins
 
        pos, hi = 0, len(_lists)
        while pos + 1 < hi:
            mi = (pos + hi) >> 1
            if value < _mins[mi]:
                hi = mi
            else:
                pos = mi
 
        _list = _lists[pos]
        lo, idx = -1, len(_list)
        while lo + 1 < idx:
            mi = (lo + idx) >> 1
            if value < _list[mi]:
                idx = mi
            else:
                lo = mi
 
        return pos, idx
 
    def add(self, value):
        """Add `value` to sorted list."""
        _load = self._load
        _lists = self._lists
        _mins = self._mins
        _list_lens = self._list_lens
 
        self._len += 1
        if _lists:
            pos, idx = self._loc_right(value)
            self._fen_update(pos, 1)
            _list = _lists[pos]
            _list.insert(idx, value)
            _list_lens[pos] += 1
            _mins[pos] = _list[0]
            if _load + _load < len(_list):
                _lists.insert(pos + 1, _list[_load:])
                _list_lens.insert(pos + 1, len(_list) - _load)
                _mins.insert(pos + 1, _list[_load])
                _list_lens[pos] = _load
                del _list[_load:]
                self._rebuild = True
        else:
            _lists.append([value])
            _mins.append(value)
            _list_lens.append(1)
            self._rebuild = True
 
    def discard(self, value):
        """Remove `value` from sorted list if it is a member."""
        _lists = self._lists
        if _lists:
            pos, idx = self._loc_right(value)
            if idx and _lists[pos][idx - 1] == value:
                self._delete(pos, idx - 1)
 
    def remove(self, value):
        """Remove `value` from sorted list; `value` must be a member."""
        _len = self._len
        self.discard(value)
        if _len == self._len:
            raise ValueError('{0!r} not in list'.format(value))
 
    def pop(self, index=-1):
        """Remove and return value at `index` in sorted list."""
        pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
        value = self._lists[pos][idx]
        self._delete(pos, idx)
        return value
 
    def bisect_left(self, value):
        """Return the first index to insert `value` in the sorted list."""
        pos, idx = self._loc_left(value)
        return self._fen_query(pos) + idx
 
    def bisect_right(self, value):
        """Return the last index to insert `value` in the sorted list."""
        pos, idx = self._loc_right(value)
        return self._fen_query(pos) + idx
 
    def count(self, value):
        """Return number of occurrences of `value` in the sorted list."""
        return self.bisect_right(value) - self.bisect_left(value)
 
    def __len__(self):
        """Return the size of the sorted list."""
        return self._len
 
    def __getitem__(self, index):
        """Lookup value at `index` in sorted list."""
        pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
        return self._lists[pos][idx]
 
    def __delitem__(self, index):
        """Remove value at `index` from sorted list."""
        pos, idx = self._fen_findkth(self._len + index if index < 0 else index)
        self._delete(pos, idx)
 
    def __contains__(self, value):
        """Return true if `value` is an element of the sorted list."""
        _lists = self._lists
        if _lists:
            pos, idx = self._loc_left(value)
            return idx < len(_lists[pos]) and _lists[pos][idx] == value
        return False
 
    def __iter__(self):
        """Return an iterator over the sorted list."""
        return (value for _list in self._lists for value in _list)
 
    def __reversed__(self):
        """Return a reverse iterator over the sorted list."""
        return (value for _list in reversed(self._lists) for value in reversed(_list))
 
    def __repr__(self):
        """Return string representation of sorted list."""
        return 'SortedList({0})'.format(list(self))

"""
Is it possible to achieve X books?
Longest contiguous subarray where all elements differ by at most K

At each index, how far to the right can I go? I can go at least as far as previously, but can I go further?

"""

def solve():
    N, K = getInts()
    H = getInts()
    ans = []
    i = 0
    j = -1
    els = SortedList([])
    best = -10**18
    best_inds = [(-1,-1)]
    while i < N:
        while j+1 < N and (len(els) == 0 or (H[j+1] <= els[0]+K and H[j+1] >= els[-1]-K)):
            j += 1
            els.add(H[j])
        ans.append(j-i+1)
        if j-i+1 > best:
            best = j-i+1
            best_inds = [(i+1,j+1)]
        elif j-i+1 == best:
            best_inds.append((i+1,j+1))
        els.remove(H[i])
        i += 1
    print(best,len(best_inds))
    for a,b in best_inds:
        print(a,b)
    return
#for _ in range(getInt()):
#print(solve())
solve()


#print(time.time()-start_time)