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Problem · Math

City Infection Number

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ArcesiumINTERNOA

Problem statement

An infinite row of cities is indexed from 0. Each city is either healthy (0) or infected (1).

On day 1, only city 0 is infected. For every later day, the state of city i is the XOR of the previous-day states of cities i - 1 and i. Treat city -1 as always healthy.

After day n, interpret the city states as a binary number with city 0 as the least significant bit. Return that number modulo 10^9 + 7.

Function

infectedCitiesValue(n: int) → int

Examples

Example 1

n = 6return = 51

The states from city 0 through city 5 are 1, 1, 0, 0, 1, 1. With city 0 as the least significant bit, the value is 1 + 2 + 16 + 32 = 51.

Example 2

n = 1return = 1

Only city 0 is infected on day 1.

Constraints

1 <= n <= 10^6.