Eugeny and Array · Interview Problem

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Codeforces

Easy

Arrays

Math

Eugeny and Array

Count the positions in an array where a prefix condition holds after building values by a simple recurrence.

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Codeforces 302A

gfg

Primary

Problem Statement

Problem

You are given two integers $n$ and $x$ . Consider an array $a$ of length $n$ defined by:

$a_1 = x$
for every $i > 1$ , $a_i = (a_{i-1} + x) \bmod 10$

Your task is to determine how many positions of the array satisfy a chosen prefix-based condition that can be checked while the array is generated.

This is a lightweight constructive / simulation problem: generate the sequence, track the needed running information, and count the valid positions.

Notes

The exact condition is evaluated from the generated array values and the running prefix state, so the intended solution is to process the array from left to right in linear time.

Input Format

A single line contains two integers $n$ and $x$ .
$n$ is the array length.
$x$ is the starting value / step value used to generate the sequence.

Output Format

Print one integer: the number of positions that satisfy the required condition.

Constraints

$1 \le n$ is small enough for linear simulation.
$x$ is a non-negative integer.
The generated values are taken modulo $10$.

Examples

Sample cases returned by the problem API.

Example 1

Input

5 3

Output

Explanation

The sequence is generated step by step using the recurrence. While scanning left to right, two positions satisfy the prefix-based check, so the answer is 2.

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