sum two string have 30 digits (example input:1,3 out put 1+3=4),how do i fix it ?

Question

#include<iostream>
#include<string.h>
using namespace std;
int main()
{
bool correct = true;
char a[31],b[31],c[33];
cout<<"enter two number\n";
cout<<"a = ";
cin>>a;
cout<<"b = ";
cin>>b;
int i,l,L;double n=0,m=0,sum = 0;
l = strlen(a);
L = strlen(b);
for(i=0 ; i<31 ; i++)
{
if(a[i]>='0'&&a[i]<='9')
n = n*10 + (a[i]-'0');
}
for(i=0 ; i<31 ; i++)
{
if(b[i]>='0' && b[i]<='9')
m = m*10 + (b[i]-'0');
}

for(i=0 ; i<33 ; i++)
{
c[i] = a[i]+b[i];
if(c[i]>'9')
c[i] = c[i]%10;
c[i+1]= c[i+1]+1;
}
for(i=0 ; i<33 ; i++)
{
if(c[i]>='0' && c[i]<=9)
sum = sum*10 + (c[i]-'0');
}
cout<<"sum = "<<sum;
}
\\what is wrong my program