Problem: This is an interactive problem.

In the Wonderful Metropolis of the Future, there is no need in subway train drivers. Due to the technological progress, they were replaced by the Artificial Intelligence (AI). Unfortunately, one day the predictions of sci-fi writers came true: the AI rebelled and now there is an uncontrollable train in the subway. It can be dangerous! Your task is to find the train and stop the AI.

The subway of the Metropolis is one line (regular straight line with no self-intersections) with n stations, indexed consecutively from 1 to n. At each moment the train is at some station. You need to determine the index of this station, so that the train would be secured.

To find the train, dispatcher Sarah gave you a gadget that allows you to select arbitrary numbers l and r (l ≤ r), and then check, whether the train is located on a station with index between l and r, inclusive. Unfortunately, recharging of the gadget takes some time (and every time you use it as soon as possible), so between two applications of the gadget the train can move to any station that is at most k stations away. Formally, if the train was at the station x when the gadget was applied, then at the next application of the gadget the train can appear at any station y such that max(1, x - k) ≤ y ≤ min(n, x + k).

Note that AI is not aware that you are trying to catch the train, so it makes all moves according to its predefined plan.

After an examination of the gadget you found that it is very old and can hold no more than 4500 applications, after which it will break and your mission will be considered a failure.

Can you find the station with the train using no more than 4500 applications of the gadgets?

Input

The first line contains two integers n and k (1 ≤ n ≤ 10^{18}, 0 ≤ k ≤ 10) — the number of stations and the maximum number of stations the train can move between two applications of the gadget.

Interaction

You can apply the gadget at most 4500 times. In order to apply the gadget you need to print two space-separated integers l and r (1 ≤ l ≤ r ≤ n). You will then receive either string "Yes", if the train is between stations l and r, inclusive, or string "No" otherwise. If l = r and you received "Yes", then you found the train successfully, and your program must halt immediately.

Answer "Bad" instead of "Yes" or "No" means that you made an invalid query or made too many queries. Exit immediately after receiving "Bad" and you will see Wrong answer verdict. Otherwise you can get an arbitrary verdict because your solution will continue to read from a closed stream.

After printing a query do not forget to output end of line and flush the output. Otherwise you will get Idleness limit exceeded. To do this, use:

  * fflush(stdout) or cout.flush() in C++; 
  * System.out.flush() in Java; 
  * flush(output) in Pascal; 
  * stdout.flush() in Python; 
  * see documentation for other languages. 



Hacks

In order to hack, you should present a test in the following format.

The first line should contain three integers n, k and p (1 ≤ n ≤ 10^{18}, 0 ≤ k ≤ 10, 1 ≤ p ≤ n) — the number of stations, the maximum number of stations the train can move between two applications of the gadget and the initial position of the train, respectively.

Each of the next 4500 lines should contain a single integer x (1 ≤ x ≤ n) — the positions of the train after each query. Two consecutive positions (including the initial one) should not differ by more than k.

For example, the following lines are the first lines of the sample test.
    
    
      
    10 2 5  
    5  
    3  
    5  
    7  
    7  
    ...  
    

Example

Input

10 2

Yes

No

Yes

Yes


Output

3 5

3 3

3 4

5 5

Note

In the first sample, the train was initially at the station 5, after the first application of the gadget it did not move, after the second application it moved to the station 3, and after the third application moved again to the station 5.

Solution (in PYTHON):

Solution:
from sys import stderr
dbg = False
def debug(x):
    if dbg:
        print "DBG: %s" % str(x)
#super_calculations
if dbg:
    def calc(k ,l):
        #k - k, l - length
        #returns hit_chance, hit_ret, split_ret_small, split_ret_big
        return [1./l, l+2*k, l/2+2*k, -(-l/2)+2*k]

    def find_min_l_split_effect(k):
        test_l = 1
        while True:
            res = calc(k, test_l)
            if res[3]<test_l:
                debug (res)
                return test_l-1
            test_l += 1
            
    for k in xrange(0, 10+1):
        min_l_s_e = find_min_l_split_effect(k)
        print "k=%i min_l_split_effect=%i" % (k, min_l_s_e)
        hit_at = min_l_s_e - 1
        while True:
            #cal EV at hit_at
            pass
            
        optimal_hit_at = 0
        print "k=%i, optimal hit at = %i" % (k, optimal_hit_at)
        print "--------------------------"
        #raw_input()

    quit()


n, k = map(int, raw_input().split())
i_from = 1
i_to = n
q_limit = 4500
q_cnt = 0
shoots_cnt = 0

from random import random
from sys import stdout, stderr
def answer(val):
    print "%i" % val
    stdout.flush()
    quit()

def test(a, b):
    print "%i %i" % (a, b)
    stdout.flush()
    return (raw_input() == "Yes")

working_with_up_bound = False
while True:
    print >> stderr, i_from, i_to
    #if search-array is small enought
    delta_l = i_to-i_from+1
    #two next_delta may be replaced by 1 round_to_up calculation
    next_delta_small = delta_l/2
    next_delta_big = delta_l-next_delta_small
    if next_delta_big + 2*k >= delta_l:
        #random shoot
        test_to = i_from + int((i_to+1-i_from)*random())
        test_from = test_to
    else:
         #bisect-search
        if working_with_up_bound:
            test_from = i_from
            test_to = i_from + (i_to-i_from)/2
        else:
            test_from = i_to - (i_to-i_from)/2
            test_to = i_to

    q_cnt += 1
    if q_cnt > q_limit:
        #FAILED
        #DEBUG
        #why this does not work?
        #wrong output format Unexpected end of file - int64 expected
        answer(shoots_cnt)   
        
    if test_to == test_from:
        shoots_cnt += 1
        
    if test(test_from, test_to):
        #founded
        if test_from == test_to:
            #after shoot YES!!!!
            answer(test_from)
        else:
            #after search
            i_from = test_from-k
            i_to = test_to+k
            
    else:
        #not founded
        if test_from == test_to:
            #after shoot
            i_from -= k
            i_to += k
        else:
            #after search
            if working_with_up_bound:
                i_from = test_to + 1 - k
                i_to = i_to + k
            else:
                i_from = i_from - k
                i_to = test_from + k-1
            #working_with_up_bound = not working_with_up_bound

    if i_from < 1:
        i_from = 1
    if i_to > n:
        i_to = n
    
    #end while