There are m jobs to schedule on n processors. A schedule is balanced if the difference between the number of jobs scheduled on any two neighboring processors does not exceed $1.$

The kth processor is the most efficient, and thus, the maximum number of jobs should be scheduled on that processor. Find the maximum number of jobs that can be scheduled on the kth processor, such that the overall schedule remains balanced.

Note: Each processor must have at least one job scheduled

Example

Consider n$=5,$ m $=11,$ k$=3.$

Explanation:

In each schedule, there are $11$ jobs across $5-$ processors. k assumes $1-$based indexing.

The $15$t schedule is not balanced because the Sth processor has $1$ job scheduled, while the $4$th processor has $4$ jobs scheduled, their difference is $3,$ which exceeds $1.$

The $5$th schedule is not balanced because the difference between the $2$nd and $3$rd$,$ and between $3$rd

$3$rd and $4$th processors is more than $1.$

Amongst all balanced schedules, the maximum number of jobs that can be scheduled on the $3$rd processor is $3.$ So$,$ the answer is $3.$

Example $2$:

Explanation

Given in n$=5,$ m $=11,$ k$=5.$

One optimal schedule is $[1,1,2,3,4]$

so $5$th process executes $4$ jobs maximum. so output is $4$

Example $3$:

Explanation

Given in n$=5,$ m $=16,$ k$=2.$

One optimal schedule is $[4,4,3,3,2]$

so $5$th process executes $4$ jobs maximum. so output is $4$

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