Symmetry

Farmer John loves symmetry and is arranging his cows on a field partitioned into an $N \times M$ grid ($1 \le N \le 10^9$, $1 \le M \le 10^9$).

To preserve symmetry, he places cows as follows. He puts one cow on the exact center square of the field; if the field has no center square, he stops. He then splits the field into four equally sized subfields, separated by the row and column of the center cow, and arranges cows on each subfield in the same way. He repeats this on ever-smaller subfields until a subfield has no center square or can no longer be divided.

A field has a center square only when both of its side lengths are odd. Splitting an $N \times M$ field (with $N$ and $M$ both odd) produces four subfields of size $\frac{N-1}{2} \times \frac{M-1}{2}$.

For example, if $N = 7$ and $M = 15$, Farmer John places a cow at row 4, column 8, then processes each resulting $3 \times 7$ subfield; in each $3 \times 7$ subfield he places a cow at row 2, column 4 and processes each resulting $1 \times 3$ subfield. The process is shown below (C denotes a cow):

...............    ...............    .......|.......    .C.|.C.|.C.|.C.
...............    ...............    ...C...|...C...    ---C---|---C---
...............    ...............    .......|.......    .C.|.C.|.C.|.C.
............... -> .......C....... -> -------C------- -> -------C-------
...............    ...............    .......|.......    .C.|.C.|.C.|.C.
...............    ...............    ...C...|...C...    ---C---|---C---
...............    ...............    .......|.......    .C.|.C.|.C.|.C.

This field needs 21 cows. In contrast, if $N = M = 5$, only one cow is needed, because the resulting $2 \times 2$ subfields have no center square. Help Farmer John determine how many cows he needs.

A single line with two space-separated integers $N$ and $M$.

The number of cows needed, on a single line.