Ciel and Dancing
Description
Fox Ciel and her friends are in a dancing room. There are n boys and m girls here, and they never danced before. There will be some songs, during each song, there must be exactly one boy and one girl are dancing. Besides, there is a special rule:
- either the boy in the dancing pair must dance for the first time (so, he didn't dance with anyone before);
- or the girl in the dancing pair must dance for the first time.
Help Fox Ciel to make a schedule that they can dance as many songs as possible.
The first line contains two integers n and m (1 ≤ n, m ≤ 100) — the number of boys and girls in the dancing room.
In the first line print k — the number of songs during which they can dance. Then in the following k lines, print the indexes of boys and girls dancing during songs chronologically. You can assume that the boys are indexed from 1 to n, and the girls are indexed from 1 to m.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 100) — the number of boys and girls in the dancing room.
Output
In the first line print k — the number of songs during which they can dance. Then in the following k lines, print the indexes of boys and girls dancing during songs chronologically. You can assume that the boys are indexed from 1 to n, and the girls are indexed from 1 to m.
Samples
2 1
2
1 1
2 1
2 2
3
1 1
1 2
2 2
Note
In test case 1, there are 2 boys and 1 girl. We can have 2 dances: the 1st boy and 1st girl (during the first song), the 2nd boy and 1st girl (during the second song).
And in test case 2, we have 2 boys with 2 girls, the answer is 3.