Fibonacci-like sequences

Inspired by the Fibonacci sequence
$F_0 = 0, F_1 = 1, F_n = F_{n-1} + F_{n-2} \mbox{\, for \,} n \ge 2$,
Xavier defined his own sequence of numbers:
$$X_0 = 0, X_1 = 1, X_n = X_{X_{n-1}} + X_{X_{n-2}} \mbox{\, for \,} n \ge 2 .$$
Max also wanted his own sequence of numbers, so he modified Xavier’s
definition a bit:
$$M_0 = 1, M_1 = 0, M_n = M_{M_{n-1}} + M_{M_{n-2}} \mbox{\, for \,} n \ge 2 .$$
Can you compute the n-th term of any of these two new sequences?

Input

Input consists of several cases, each with a character c, which is ‘X’
or ‘M’, and a natural n between 0 and 10⁹.

Output

For each case, print X_(n) or M_(n) depending on c.

Problem information

Author: Félix Moreno

Generation: 2026-01-25T11:35:11.622Z

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