```
def power(a,b):
if b==0:
return 1
res=power(a,int(b/2))
if b%2==1:
return res*res*a
else:
return res*res
t=int(input())
for i in range(0,t):
n=int(input())
a=list(map(int,input().split()))
a.sort()
d={}
for i in range(0,n+2):
if i==0:
d[i]=1
else:
d[i]=0
for i in range(0,n):
if a[i]>n:
a[i]=n+1
d[a[i]]=d[a[i]]+1
total=0
val=1
m=0
#print(d)
for i in range(1,n+2):
val=val*(power(2,d[i-1])-1)
m=m+d[i]
total=total+i*(power(2,n-m))*val
#print(i,"values",m,val,(2**(n-m))*val)
print(total%998244353)
```

This was solution for MEXUM( MEXUM Problem - CodeChef )

solution link : CodeChef: Practical coding for everyone

I am getting a AC in subtask1 but TLE in subtask2.

Kindly Suggest Optimizations in the code.

( Thanks @anon71312354 for your help in correcting my modulo mistake )

Modulo!?

I don’t know much about integer limits in Python, but the answer is going to be a huge one. I suggest you take modulo at every step.

Plus, the TL in bigger case is probably because of you exponent time complexity. Simply taking power is costly. Make your own modulo exponent function that works in logN.

```
const int MOD = 998244353;
typedef long long ll;
ll powN(ll a,ll p)
{
if(p==0) return 1;
ll z=powN(a,p/2);
z=(z*z)%MOD;
if(p%2) z=(z*a)%MOD;
return z;
}
```

This is an example code for C++. I hope you can translate that to Python quite easily.

thank you anand, the modulo mistake was really a stupid one, i will try the modulo exponent function and try the same

anand i corrected the modulo mistake and got AC in the subtask1, and i also used binary exponentiation for the power function as suggested by you, still i am getting a TLE for subtask2.

Can anyone please suggest a even further optimization.

```
def power(a,b):
if b==0:
return 1
res=power(a,int(b/2))
if b%2==1:
return res*res*a
else:
return res*res
t=int(input())
for i in range(0,t):
n=int(input())
a=list(map(int,input().split()))
a.sort()
d={}
for i in range(0,n+2):
if i==0:
d[i]=1
else:
d[i]=0
for i in range(0,n):
if a[i]>n:
a[i]=n+1
d[a[i]]=d[a[i]]+1
total=0
val=1
m=0
#print(d)
for i in range(1,n+2):
val=val*(power(2,d[i-1])-1)
m=m+d[i]
total=total+i*(power(2,n-m))*val
#print(i,"values",m,val,(2**(n-m))*val)
print(total%998244353)
```

solution link: CodeChef: Practical coding for everyone

I would recommend using the inbuilt pow

`pow(a,b,c)`

gives a^b \mod c. Unlike C++, in python `pow()`

is actually useful. Secondly take modulo at every step, not just the last step, because the numbers are becoming very big.

i used the inbuilt pow function before this @everule1 but got TLE even then.

But i will try taking modulo at each step as you suggested.

It won’t give you TLE if you pass c=998244353 and take mod at each step. Also you should probably declare some variable like mod=998244353.

i did this and got an AC. Thank you @everule1

But i am not able to understand why this happened, because the complexity of the main code doesn’t change if i introduce a mod at each step end, that just helps to prevent overflow, how does the time taken reduce?

```
mod=998244353
t=int(input())
for i in range(0,t):
n=int(input())
a=list(map(int,input().split()))
a.sort()
d={}
for i in range(0,n+2):
if i==0:
d[i]=1
else:
d[i]=0
for i in range(0,n):
if a[i]>n:
a[i]=n+1
d[a[i]]=d[a[i]]+1
total=0
val=1
m=0
#print(d)
for i in range(1,n+2):
val=val*(pow(2,d[i-1],mod)-1)
m=m+d[i]
total=(total+i*(pow(2,n-m,mod))*val)%mod
#print(i,"values",m,val,(2**(n-m))*val)
print(total%mod)
```

this is my new code

In python numbers which cannot be handled by 64 bits are handled differently. Instead of being direrctly handled by the CPU, the calculations are performed in a much more tedious way. This makes addition,subtraction,multiplication,division and modulo on such huge numbers take a lot more time than numbers which fit in 64 bits.

You can read more about it here

https://www.reddit.com/r/Python/comments/39p57f/how_can_python_deal_with_bigger_numbers_than/

There’s a very simple way to understand. What will take more time, multiplying 9 digit integers, or 10^5 digit integers?

Thank you @everule1 @bravotango, i understand the process now.