can anyone plzz exaplin me the solution for the yesterday’s contest thankyou ?

By looking at the equation we can say that if k is less then the value of x will be more (as the number of terms will be more) so for finding the maximum value of k we have to make our x small .

consider x = 0 then on the right side of the equation there will be only one term whose value is 1 independent of the value of n+k so we cannot get 2^n

now consider x = 1 we can get 2^n as

C(n,r) represents r combinations out of n things

```
C(n+k,0) + C(n+k,1) = 2^n C(n,0) will always be 1
C(n+k,1) = 2^n - 1 C(n,1) will always be n
n + k = 2^n - 1
k = 2^n - 1 - n
first find 2^n % 1000000007 using fast exponentiation
an then substract n+1 from that
```

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thanks for this much details

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thnkss bro