1 /*
2 HDU5976 Detachment
3 http://acm.hdu.edu.cn/showproblem.php?pid=5976
4 数论 等差数列
5 *
6 *
7 */
8 #include <cstdio>
9 #include <algorithm>
10 #include <vector>
11 using namespace std;
12 const int mod=1000000007;
13 const int Nmax=50001;
14 vector<long long> v;
15 long long f[Nmax];
16 long long g[Nmax];
17 long long qpow(long long base,int n)
18 {
19 long long ans=1LL;
20 base=base%mod;
21 while(n>0)
22 {
23 if(n&1)
24 ans=ans*base%mod;
25 base=(base*base)%mod;
26 n>>=1;
27 }
28 while(ans<0)
29 ans+=mod;
30 return ans;
31 }
32
33 int main()
34 {
35 //freopen("3.in","r",stdin);
36 int t;
37 scanf("%d",&t);
38 long long x;
39 f[1]=1LL;
40
41 f[0]=0LL;
42 f[2]=2LL;
43 g[1]=1LL;
44 g[2]=2LL;
45 v.push_back(f[1]);
46 v.push_back(f[2]);
47 for(int i=3;i<Nmax;i++)
48 {
49 g[i]=1LL*i*g[i-1]%mod;
50 f[i]=1LL*i+f[i-1];
51 v.push_back(f[i]);
52 }
53 //printf("%lld\n",f[Nmax-1]);
54 while(t--)
55 {
56 long long ans=1LL;
57 scanf("%lld",&x);
58 int j=1;
59 int k=1;
60 for(int i=1;i<Nmax;i++)
61 {
62 if(x>=f[i] && x<f[i+1])
63 {
64 j=i;
65 break;
66 }
67 }
68 //printf("bj:%d\n",j);
69 j=lower_bound(v.begin(),v.end(),x)-v.begin();
70 while(!(x>=f[j]&& x<f[j+1]))
71 j++;
72 //printf("j:%d\n",j);
73 long long remain=x-f[j];
74 if(remain)
75 {
76 if(remain==j)
77 k=2;
78 else
79 k=j+1-remain;
80 //printf("j:%d k:%d\n",j,k);
81 ans=g[j];
82 ans=ans*qpow(1LL*k, mod-2 )%mod;
83 ans=ans*(k+remain)%mod;
84 }
85 else
86 {
87 ans=g[j];
88 }
89 while(ans<0)
90 ans+=mod;
91 printf("%lld\n",ans);
92 }
93 return 0;
94 }
