CodeForces 163A Substring and Subsequence（DP）

题意：给你两个字符串，然后问你第一个字符串的子串和第二个子序列有多少对相同的串

思路：dp[i][j]表示第一个串以i结尾，第二个串以j结尾的方案数，最简单的dp就是dp[i][j]=1+dp[i-1][j-1]+dp[i-1][j-2]+....+dp[i-1][1]，然后把前面的弄成前缀和就可以了

#include<bits/stdc++.h>
using namespace std;
#define LL long long
const int maxn = 5005;
const int mod = 1e9+7;
int dp[maxn][maxn];
char a[maxn],b[maxn];
int main()
{
scanf("%s%s",a+1,b+1);
int len1 = strlen(a+1);
int len2 = strlen(b+1);
for (int i = 1;i<=len1;i++)
{
for (int j = 1;j<=len2;j++)
{
if (a[i]==b[j])
dp[i][j]=(dp[i][j]+dp[i-1][j-1]+1)%mod;
dp[i][j]=(dp[i][j]+dp[i][j-1])%mod;
}
}
LL ans = 0;
for (int i = 1;i<=len1;i++)
ans = (ans+dp[i][len2])%mod;
printf("%lld\n",ans);
}

Description

One day Polycarpus got hold of two non-empty strings s and t, consisting of lowercase Latin letters. Polycarpus is quite good
with strings, so he immediately wondered, how many different pairs of "xy" are there, such that x is
a substring of string s, y is a subsequence of string t, and
the content of x and y is the same. Two pairs are considered different, if they contain different substrings of string s or
different subsequences of string t. Read the whole statement to understand the definition of different substrings and subsequences.

The length of string s is the number of characters in it. If we denote the length of the string s as |s|,
we can write the string as s = s1s2...s|s|.

A substring of s is a non-empty string x = s[a... b] = sasa + 1... sb (1 ≤ a ≤ b ≤ |s|).
For example, "code" and "force" are substrings or "codeforces", while "coders" is not. Two substrings s[a... b] and s[c... d] are
considered to be different if a ≠ c or b ≠ d. For example, if s="codeforces", s[2...2] and s[6...6] are
different, though their content is the same.

A subsequence of s is a non-empty string y = s[p1p2... p|y|] = sp1sp2... sp|y| (1 ≤ p1 < p2 < ... < p|y| ≤ |s|).
For example, "coders" is a subsequence of "codeforces". Two subsequences u = s[p1p2... p|u|] and v = s[q1q2... q|v|] are
considered different if the sequences p and q are different.

Input

The input consists of two lines. The first of them contains s (1 ≤ |s| ≤ 5000), and the second one contains t (1 ≤ |t| ≤ 5000).
Both strings consist of lowercase Latin letters.

Output

Print a single number — the number of different pairs "xy" such that x is
a substring of string s, y is a subsequence of string t, and
the content of x and y is the same. As the answer can be rather large, print it modulo 1000000007(109 + 7).

Sample Input

Input

aa
aa

Output

5

Input

codeforces
forceofcode

Output

60

Hint

Let's write down all pairs "xy" that form the answer in the first sample: "s[1...1]t[1]",
"s[2...2]t[1]", "s[1...1]t[2]","s[2...2]t[2]",
"s[1...2]t[1 2]".