Along a long border wall stand n numbered watchtowers, numbered 0 to n-1 from one end of the wall to the other. On a given night, each tower either lights a signal beacon or stays dark; this is recorded as a sequence of n values, one per tower, where 1 means the tower's beacon is lit that night and 0 means it stays dark. To keep two beacons' smoke plumes from drifting into each other, wall regulations require that between any two lit towers there be at least k dark towers separating them — equivalently, if two lit towers sit at indices a and b with a < b, then b - a must be at least k + 1.

Given the night's sequence and the required minimum k, determine whether every pair of lit towers that night satisfies the spacing rule.

Input format

The first line contains two integers n and k. The second line contains n integers, each either 0 or 1, describing the state of each tower in order.

Output format

Print a single line containing exactly true if every two lit towers are at least k towers apart (in the sense above), or false otherwise.

Constraints

• 1 <= n <= 100000
• 0 <= k <= n
• each of the n values is 0 or 1

10 2
0 1 0 0 0 1 0 0 1 0

true

6 2
1 0 0 1 0 1

false