1.4.1 Arithmetic Progressions

  
    

   
     
/*
   
     
ID: awsd1231
   
     
PROG: ariprog
   
     
LANG: C++
   
     
*/
   
     
#include<iostream>
   
     
#include<cstdio>
   
     
#include<algorithm>
   
     
#include<set>
   
     

   
     
using namespace std;
   
     

   
     
int n, m;//等差数列长度，双平方数上界
   
     
struct T {
   
     
 int a, b;
   
     
}ans[10005];
   
     

   
     
bool may[125005] = {0};
   
     
set<int> list;
   
     

   
     
void fill(int x) {
   
     
 int t = 0;
   
     
 for(int i = 0; i != x + 1; ++i) 
   
     
 for(int j = 0; j != x + 1; ++j) {
   
     
 may[i*i + j*j] = 1;
   
     
 list.insert(i*i + j*j);
   
     
 }
   
     
}
   
     

   
     
bool check(int x, int y) {
   
     
 int ni = 0;
   
     
 while(ni != n){
   
     
 // if(!may[x + (n - 2) * y])return false;
   
     
 if(may[x + ni * y]) ++ni;
   
     
 else return false;
   
     
 }return true;
   
     
}
   
     

   
     
bool operator < (T a, T b) {
   
     
 if(a.b != b.b) return a.b < b.b;
   
     
 return a.a < b.a;
   
     
}
   
     

   
     
int main() {
   
     
 freopen("ariprog.in", "r", stdin);
   
     
 freopen("ariprog.out", "w", stdout);
   
     
 cin >> n >> m;
   
     
 fill(m);
   
     
 int idx = 0, t = 0;
   
     
 set<int>::iterator lis = list.begin();
   
     
 for(int a = *lis; a < m*m*2-1; a = *(++lis)) {
   
     
 for(int b = 1; b != (2*m*m - a) / (n-1) + 1; ++b) {
   
     
 if(check(a, b)) {
   
     
 ans[idx].a = a;
   
     
 ans[idx++].b = b;
   
     
 }
   
     
 }
   
     
 }
   
     
 if(idx) {
   
     
 sort(ans, ans+idx);
   
     
 for(int i = 0; i != idx; ++i) {
   
     
 cout << ans[i].a << " " << ans[i].b << endl;
   
     
 }
   
     
 }else 
   
     
 cout << "NONE" << endl;
   
     
 return 0;
   
     
}
  
    

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