when I changed

char buf[100];
cin.getline(buf, 100);

to

char buf[1000];
cin.getline(buf, 1000);

I got AC, but problem statement says that polynom's length is no longer than 100 characters.

Because there is a '\0' character in the end of string, so for string with length 100 you should use "char buf[101]".

And, when you use cin.getline() to read a line of max-length 100, you should write:
cin.getline(*, 101, '\n');
instead of
cin.getline(*, 100, '\n');