https://hihocoder.com/problemset/problem/1430
思路：
要用前缀去推Sigma总公式，比较方便。https://blog.csdn.net/weixin_37517391/article/details/83821752
1 #define IOS ios_base::sync_with_stdio(0); cin.tie(0);
2 #include <cstdio>//sprintf islower isupper
3 #include <cstdlib>//malloc exit strcat itoa system("cls")
4 #include <iostream>//pair
5 #include <fstream>//freopen("C:\\Users\\13606\\Desktop\\草稿.txt","r",stdin);
6 #include <bitset>
7 //#include <map>
8 //#include<unordered_map>
9 #include <vector>
10 #include <stack>
11 #include <set>
12 #include <string.h>//strstr substr
13 #include <string>
14 #include <time.h>//and(((unsigned)time(NULL))); Seed n=rand()%10 - 0~9;
15 #include <cmath>
16 #include <deque>
17 #include <queue>//priority_queue<int, vector<int>, greater<int> > q;//less
18 #include <vector>//emplace_back
19 //#include <math.h>
20 //#include <windows.h>//reverse(a,a+len);// ~ ! ~ ! floor
21 #include <algorithm>//sort + unique : sz=unique(b+1,b+n+1)-(b+1);+nth_element(first, nth, last, compare)
22 using namespace std;//next_permutation(a+1,a+1+n);//prev_permutation
23 #define rint register int
24 #define fo(a,b,c) for(rint a=b;a<=c;++a)
25 #define fr(a,b,c) for(rint a=b;a>=c;--a)
26 #define mem(a,b) memset(a,b,sizeof(a))
27 #define pr printf
28 #define sc scanf
29 #define ls rt<<1
30 #define rs rt<<1|1
31 typedef long long ll;
32 void swapp(int &a,int &b);
33 double fabss(double a);
34 int maxx(int a,int b);
35 int minn(int a,int b);
36 int Del_bit_1(int n);
37 int lowbit(int n);
38 int abss(int a);
39 const double E=2.718281828;
40 const double PI=acos(-1.0);
41 //const ll INF=(1LL<<60);
42 const int inf=(1<<30);
43 const double ESP=1e-9;
44 const int mod=(int)1e9+7;
45 const int N=(int)5e4+10;
46
47 long long C[110][110];
48 void Init() {
49 C[0][0] = 1;
50 for(int i = 1;i <= 100;++i) {
51 C[i][0] = 1;
52 for(int j = 1;j <= i;++j) {
53 C[i][j] = (C[i-1][j-1] + C[i-1][j]) % mod;
54 }
55 }
56 }
57 //======================================================Cnk预处理;
58 ll S[105][N],SS[105][N],ans[N];
59 char s[N];
60
61 void solve()
62 {
63 ll n,k;
64 sc("%lld%lld",&n,&k);
65 sc("%s",s);
66
67 for(int i = 0;i <= n;++i) S[0][i] = 1;
68 for(int i = 1;i <= n;++i) S[1][i] = (s[i-1]-'0') + S[1][i-1] ;
69 for(int i = 2;i <= k;++i)
70 for(int j = 1;j <= n;++j)
71 S[i][j] = S[1][j] * S[i-1][j] % mod;
72
73 SS[0][0] = 1;
74
75 for(int i = 0;i <= k;++i) {
76 for(int j = 1;j <= n;++j)
77 SS[i][j] = (SS[i][j-1] + S[i][j])%mod;
78 }
79
80 for(int i=1;i<=n;++i)
81 {
82 ll sum=0;
83 for(int j=0;j<=k;++j)
84 {
85 ll temp=C[k][j]*S[k-j][i]%mod*SS[j][i-1]%mod;
86 if(j&1)
87 sum=(sum-temp+mod)%mod;
88 else
89 sum=(sum+temp)%mod;
90 }
91 ans[i]=sum;
92 }
93 for(int i=1;i<=n;++i)
94 pr("%lld%c",ans[i],i==n?'\n':' ');
95 }
96
97 int main()
98 {
99 Init();
100 int T;
101 sc("%d",&T);
102 while(T--)solve();
103 return 0;
104 }
105
106 /**************************************************************************************/
107
108 int maxx(int a,int b)
109 {
110 return a>b?a:b;
111 }
112
113 void swapp(int &a,int &b)
114 {
115 a^=b^=a^=b;
116 }
117
118 int lowbit(int n)
119 {
120 return n&(-n);
121 }
122
123 int Del_bit_1(int n)
124 {
125 return n&(n-1);
126 }
127
128 int abss(int a)
129 {
130 return a>0?a:-a;
131 }
132
133 double fabss(double a)
134 {
135 return a>0?a:-a;
136 }
137
138 int minn(int a,int b)
139 {
140 return a<b?a:b;
141 }