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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

A single line contains integers i and L (0 ≤ i ≤ 9999; 1 ≤ L ≤ 14).

### 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
Tags: none