SkyWT

Fighting 2019!

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Ivan wants to make a necklace as a present to his beloved girl. A necklace is a cyclic sequence of beads of different colors. Ivan says that necklace is beautiful relative to the cut point between two adjacent beads, if the chain of beads remaining after this cut is a palindrome (reads the same forward and backward).

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Yaroslav has n points that lie on the Ox axis. The coordinate of the first point is x_1, the coordinate of the second point is x_2, ..., the coordinate of the n-th point is — x_n. Now Yaroslav wants to execute m queries, each of them is of one of the two following types:

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In mathematical terms, the sequence F_n of Fibonacci numbers is defined by the recurrence relation

F_1 = 1; F_2 = 1; F_n = F_{n - 1} + F_{n - 2} (n > 2)

DZY loves Fibonacci numbers very much. Today DZY gives you an array consisting of n integers: a_1, a_2, \dots, a_n. Moreover, there are m queries, each query has one of the two types:

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The cool breeze blows gently, the flowing water ripples steadily.

"Flowing and passing like this, the water isn't gone ultimately; Waxing and waning like that, the moon doesn't shrink or grow eventually."
"Everything is transient in a way and perennial in another."

Kanno doesn't seem to make much sense out of Mino's isolated words, but maybe it's time that they enjoy the gentle breeze and the night sky — the inexhaustible gifts from nature.

Gazing into the sky of stars, Kanno indulges in a night's tranquil dreams.

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