Prateek is an exceptionally talented student who excels in various mathematical disciplines such as Combinatorics, Algebra, Number Theory, Geometry, and Calculus. Not only is he intelligent, but he is also incredibly fast! One day, Prateek decided to determine if anyone could possibly perform calculations faster than him. To do so, he organized a highly competitive contest and invited participants to take part. In this contest, Prateek provided the contestants with numerous pairs of numbers. Each number is composed of only 0s and 1s. The contestants were required to generate a new number based on the given pair of numbers. The rule was simple: the i-th digit of the answer should be 1 if and only if the i-th digit of the two given numbers differ. Otherwise, the i-th digit of the answer should be 0. Prateek created many numbers and initially tested his own speed. He discovered that he could perform these operations on numbers of infinite length in an instant! Since he always provides correct answers, he expects the contestants to do the same. Prateek is fair and does not provide excessively large numbers, ensuring that each contestant receives numbers of the same length. Now, it's your turn to participate in Prateek's contest. Let's see if you can be faster and more accurate!