CodeForces 595B Pasha and Phone

迈不过友情╰ 2022-08-22 15:19 8阅读 0赞

# **CodeForces 595B Pasha and Phone** #

Time Limit:1000MS Memory Limit:262144KB 64bit IO Format:%I64d & %I64u

## Description ##

Pasha has recently bought a new phone jPager and started adding his friends’ phone numbers there. Each phone number consists of exactly n digits.

Also Pasha has a number k and two sequences of length n / k (n is divisible by k) a1, a2, ...,an / k and b1,b2, ...,bn / k. Let’s split the phone number into blocks of length k. The first block will be formed by digits from the phone number that are on positions 1, 2,…, k, the second block will be formed by digits from the phone number that are on positions k + 1, k + 2, …, 2·k and so on. Pasha considers a phone number good, if the i-th block doesn’t start from the digit bi and is divisible by ai if represented as an integer.

To represent the block of length k as an integer, let’s write it out as a sequence c1, c2,…,ck. Then the integer is calculated as the result of the expression c1⋅10k−1\+c2⋅10k−2\+…ck.

Pasha asks you to calculate the number of good phone numbers of length n, for the given k, ai and bi. As this number can be too big, print it modulo 109\+7.

## Input ##

The first line of the input contains two integers n and k (1 ≤ n ≤ 100 000, 1 ≤ k ≤ min(n, 9)) — the length of all phone numbers and the length of each block, respectively. It is guaranteed that n is divisible by k.

The second line of the input contains n / k space-separated positive integers — sequence a1, a2, ...,an / k (1 ≤ ai< 10k).

The third line of the input contains n / k space-separated positive integers — sequence b1,b2, ...,bn / k (0 ≤bi ≤ 9).

## Output ##

Print a single integer — the number of good phone numbers of length n modulo 109\+7.

Sample Input

## Input ##

> 6 2  
> 38 56 49  
> 7 3 4

## Output ##

> 8

## Input ##

> 8 2  
> 1 22 3 44  
> 5 4 3 2

## Output ##

> 32400

## Hint ##

In the first test sample good phone numbers are: 000000, 000098, 005600, 005698, 380000, 380098, 385600, 385698

链接在这： [题目链接][Link 1]

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题意：求n位且满足以下两点的号码数量

把号码分成k份（可能以0开头）  
1. 第i份是ai的倍数；  
2. 第i份不能是以bi开头的数；

按份for循环找一遍，再取模相乘  
注意讨论bi是否为0，pow有误差。

代码：

#include<stdio.h>
    #define mod 1000000007
    int a[100005];
    int b[100005];
    int ans[100005];
    long long mypow(int a,int b)
    {
        long long ans=1;
        for(int i=0; i<b; i++)
            ans*=10;
        return ans;
    }
    int main()
    {
        int n,k;
        while(~scanf("%d %d",&n,&k))
        {
            for(int i=0; i<n/k; i++)
                scanf("%d",&a[i]);
            for(int i=0; i<n/k; i++)
                scanf("%d",&b[i]);
            for(int i=0; i<n/k; i++)
            {
                if(b[i]==0)
                {
                    ans[i]+=((mypow(10,k)-1)/a[i])+1;
                    ans[i]-=(mypow(10,k-1)-1)/a[i]+1;
                }
                else
                {
                    ans[i]+=((mypow(10,k)-1)/a[i])+1;
                    ans[i]-=(mypow(10,k-1)*(b[i]+1)-1)/a[i]-(mypow(10,k-1)*(b[i])-1)/a[i];
                }
            }
            long long ans2=1;
            for(int i=0; i<n/k; i++)
            {
                ans2*=ans[i];
                ans2%=mod;
            }
            printf("%lld\n",ans2);
        }
        return 0;
    }

[Link 1]: http://codeforces.com/problemset/problem/595/B