Write a C++ program that defines a class BigInteger that stores arbitrarily large integers by keeping their digits in a vector. Supply a constructor BigInteger(string) that reads a sequence of digits from a string. Overload the +, -, and * operators to add, subtract, and multiply the digit sequences. Overload the << operator to send the big integer to a stream. For example,

BigInteger a("123456789");

BigInteger b("987654321");

cout << a * b;

prints 121932631112635269.