Can All Packages Be Delivered

Each time, deliver one package with any truck whose current capacity is sufficient; that truck's capacity then becomes its current capacity divided by 2, rounded down. Packages may be delivered in any order; determine whether all of them can be delivered. Each test case on this site gives one independent scenario, corresponding to a single scenario among the source's multiple scenarios.

输入格式

The first line contains n m (both 1..100000), the second line contains n capacities, and the third line contains m weights, all 1..10⁹.

输出格式

Output a single integer answer.

样例 1

输入：

1 4
8
8 4 2 1

输出：

1

样例 2

输入：

1 2
3
2 2

输出：

0

样例 3

输入：

2 2
4 3
3 4

输出：

1

样例说明

Example 1: the only truck's capacity goes 8, 4, 2, 1, exactly enough to deliver everything, so output 1. Example 2: after delivering 2 the capacity is only 1, so the second 2 cannot be delivered; output 0. Example 3: capacity 4 delivers weight 4 and capacity 3 delivers weight 3; output 1.