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1064. Binary Search

Time limit: 1.0 second
Memory limit: 64 MB
The program fragment below performs binary search of an integer number in an array that is sorted in a nondescending order:

Pascal

procedure BinarySearch(x: integer; N: integer; A: array of 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++

void BinarySearch(int x, int N, int* A)
{
    int p = 0;     // Left border of the search
    int q = N - 1; // Right border of the search
    int L = 0;     // Comparison counter
    while (p <= q) {
        int 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;
    }
}

Python

def BinarySearch(x: int, N: int, A: list):
    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 += 1
        if A[i] == x:
            print('Found item i =', i, 'in L =', L, 'comparisons')
            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 of length N.
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 values of N 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 ≤ 9999; 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 shall contain the single 0.

Samples

inputoutput
9000 2
0
10 3
4
12 12
17 18
29 30
87 94
Problem Source: 2000-2001 ACM Northeastern European Regional Programming Contest