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Oct 17th, 2020
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  1. /*
  2. _____ _ _ _ _
  3. |_ _| |__ ___ / \ _ __ ___| |__ _ _| |
  4. | | | '_ \ / _ \ / _ \ | '_ \/ __| '_ \| | | | |
  5. | | | | | | __// ___ \| | | \__ \ | | | |_| | |
  6. |_| |_| |_|\___/_/ \_\_| |_|___/_| |_|\__,_|_|
  7.  
  8. */
  9. #include<bits/stdc++.h>
  10. #include <ext/pb_ds/assoc_container.hpp>
  11. #include <ext/pb_ds/tree_policy.hpp>
  12. #define ll long long
  13. #define pb push_back
  14. #define ppb pop_back
  15. #define endl '\n'
  16. #define mii map<ll,ll>
  17. #define msi map<string,ll>
  18. #define mis map<ll, string>
  19. #define rep(i,a,b) for(ll i=a;i<b;i++)
  20. #define repr(i,a,b) for(ll i=b-1;i>=a;i--)
  21. #define trav(a, x) for(auto& a : x)
  22. #define pii pair<ll,ll>
  23. #define vi vector<ll>
  24. #define vii vector<pair<ll, ll>>
  25. #define vs vector<string>
  26. #define all(a) (a).begin(),(a).end()
  27. #define F first
  28. #define S second
  29. #define sz(x) (ll)x.size()
  30. #define hell 1000000007
  31. #define lbnd lower_bound
  32. #define ubnd upper_bound
  33. #define max(a,b) (a>b?a:b)
  34. #define min(a,b) (a<b?a:b)
  35.  
  36. /* For Debugging */
  37. #define DEBUG cerr<<"\n>>>I'm Here<<<\n"<<endl;
  38. #define display(x) trav(a,x) cout<<a<<" ";cout<<endl;
  39. #define what_iss(x) cerr << #x << " = " << x << endl;
  40. #define what_is(x) cerr << #x << " = " << x << " ";
  41.  
  42. std::mt19937_64 rng(std::chrono::steady_clock::now().time_since_epoch().count());
  43. #define ordered_set tree<ll, null_type,less<ll>, rb_tree_tag,tree_order_statistics_node_update>
  44. #define TIME cerr << "\nTime elapsed: " << setprecision(5) <<1000.0 * clock() / CLOCKS_PER_SEC << "ms\n";
  45. #define DECIMAL(n) cout << fixed ; cout << setprecision(n);
  46. #define FAST ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
  47. using namespace __gnu_pbds;
  48. using namespace std;
  49. #define PI 3.141592653589793
  50. #define N 100005
  51. #define M 60
  52.  
  53. long long pw[M];
  54. vector<vi> mat2D[M];
  55.  
  56. ll mul(ll p1,ll p2) {
  57. long long num1 = p1,num2 = p2;
  58. num1 = (num1 * num2) % hell;;
  59. return (int) num1;
  60. }
  61.  
  62. ll add(ll p1, ll p2) {
  63. if( p1 + p2 >= hell) {
  64. return p1 + p2 - hell;
  65. return (p1 + p2);
  66. }
  67. }
  68.  
  69. vector<vi> mul(vector<vi> p1, vector<vi> p2) {
  70. vector<vi> tmp(2,vi(2,0));
  71. rep(i,0,2) {
  72. rep(j,0,2) {
  73. tmp[i][j] = 0;
  74. rep(k,0,2) {
  75. tmp[i][j] = add(tmp[i][j], mul(p1[i][k] , p2[k][j]));
  76. }
  77. }
  78. }
  79. return tmp;
  80. }
  81.  
  82.  
  83. vector<vi> expo(vector<vi> base, ll exponent, ll mod) { //return base^exponent modulo modulus
  84. vector<vi> ans {{1,0},{0,1}};
  85. rep(i,0,M) {
  86. if(exponent & pw[i]) {
  87. ans = mul(ans,mat2D[i]);
  88. }
  89. }
  90. return ans;
  91. }
  92.  
  93. ll expo(ll base, ll exponent, ll mod) { //return base^exponent modulo modulus
  94. ll ans = 1;
  95. while(exponent !=0 ) {
  96. if((exponent&1) == 1) {
  97. ans = ans*base ;
  98. ans = ans%mod;
  99. }
  100. base = base*base;
  101. base %= mod;
  102. exponent>>= 1;
  103. }
  104. return ans%mod;
  105. }
  106.  
  107. void solve()
  108. {
  109. ll n;
  110. cin >> n;
  111. ll num = (n + 1) / 2;
  112. ll ans;
  113. if(num == 1) {
  114. ans = 1;
  115. } else {
  116. vector<vi> tmp = {{3,1},{hell - 1,0}};
  117. what_iss(num);
  118. tmp = expo(tmp,num, hell);
  119. ans = tmp[0][0];
  120. }
  121. ll num2 = expo(2,n - 1,hell);
  122. what_is(num2);
  123. what_iss(ans);
  124. num2 = expo(num2,hell-2,hell);
  125. ans = (ans * num2) % hell;
  126. cout << ans << endl;
  127. return;
  128. }
  129. int main()
  130. {
  131. pw[0] = 1;
  132. rep(i,1, M) {
  133. pw[i] = pw[i-1] * 2;
  134. }
  135. mat2D[0] = {{1,0},{0,1}};
  136. mat2D[1] = {{3,1},{hell - 1,0}};
  137. rep(i, 2, M) {
  138. mat2D[i] = mul(mat2D[i-1],mat2D[i-1]);
  139. }
  140.  
  141. FAST
  142. int TESTS=1;
  143. cin>>TESTS;
  144. rep(i,0,TESTS)
  145. {
  146. // cout<<"Case #"<<i+1<<": ";
  147. solve();
  148. }
  149. // TIME
  150. return 0;
  151. }
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