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ZOJ Problem Set - 2054
Binary Search

Time Limit: 2 Seconds      Memory Limit: 65536 KB

The program fragment below performs binary search of an integer number in an array that is sorted in a nondescending order:

Pascal

const
  MAXN = 10000;
var
  A: array[0..MAXN-1] of integer;
  N: integer;

procedure BinarySearch(x: integer);
var
  p, q, i, L: integer;
begin
  p := 0;   { Left border of the search  }
  q := N-1; { Right border of the search }
  L := 0;   { Comparison counter         }
  while p <= q do begin
    i := (p + q) div 2;
    inc(L);
    if A[i] = x then begin
      writeln('Found item i = ', i,
        ' in L = ', L, ' comparisons');
      exit
    end;
    if x < A[i] then
      q := i - 1
    else
      p := i + 1
  end
end;

C

#define MAXN 10000

int A[MAXN];
int N;

void BinarySearch(int x)
{
  int p, q, i, L;

  p = 0;   /* Left border of the search  */
  q = N-1; /* Right border of the search */
  L = 0;   /* Comparison counter         */
  while (p <= q) {
    i = (p + q) / 2;
    ++L;
    if (A[i] == x) {
      printf("Found item i = %d"
        " in L = %d comparisons\n", i, L);
      return;
    }
    if (x < A[i])
      q = i - 1;
    else
      p = i + 1;
  }
}

Before BinarySearch was called, N was set to some integer number from 1 to 10000 inclusive and array A was filled with a nondescending integer sequence.

It is known that the procedure has terminated with the message "Found item i = XXX in L = XXX comparisons" with some known values of i and L.

Your task is to write a program that finds all possible values of N that could lead to such message. However, the number of possible values of N can be quite big. Thus, you are asked to group all consecutive Ns into intervals and write down only first and last value in each interval.


Input

The input consists of a single line with two integers i and L (0 <= i < 10000 and 1 <= L <= 14), separated by a space.


Output

On the first line of the output write the single integer number K representing the total number of intervals for possible values of N. Then K lines shall follow listing those intervals in an ascending order. Each line shall contain two integers Ai and Bi (Ai <= Bi) separated by a space, representing first and last value of the interval.

If there are no possible values of N exist, then the output file shall contain the single 0.


This problem contains multiple test cases!

The first line of a multiple input is an integer N, then a blank line followed by N input blocks. Each input block is in the format indicated in the problem description. There is a blank line between input blocks.

The output format consists of N output blocks. There is a blank line between output blocks.


Sample Input


2

9000 2

10 3


Sample Output

0

4
12 12
17 18
29 30
87 94


Source: Northeastern Europe 2000
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