#include #include #include #include #include #include #include #include #include using namespace std; using lli = long long int; using Vint = std::vector; using Vlli = std::vector; using Wint = std::vector; using Wlli = std::vector; using Vbool = std::vector; using pii = std::pair; using pll = std::pair; constexpr int MOD = 1e9 + 7; constexpr int INFi = 2e9 + 1; constexpr lli INFl = (lli)(9e18) + 1; const vector DXDY = {std::make_pair(1, 0), std::make_pair(-1, 0), std::make_pair(0, 1), std::make_pair(0, -1)}; constexpr char BR = '\n'; #define FOR(i, a, b) for(int (i) = (a); (i) < (b); (i)++) #define FOReq(i, a, b) for(int (i) = (a); (i) <= (b); (i)++) #define rFOR(i, a, b) for(int (i) = (b); (i) >= (a); i--) #define FORstep(i, a, b, step) for(int (i) = (a); i < (b); i += (step)) #define REP(i, n) FOR(i, 0, n) #define rREP(i, n) rFOR(i, 0, (n-1)) #define vREP(ele, vec) for(auto &(ele) : (vec)) #define vREPcopy(ele, vec) for(auto (ele) : (vec)) #define SORT(A) std::sort((A).begin(), (A).end()) template inline int argmin(vector vec){return min_element(vec.begin(), vec.end()) - vec.begin();} template inline int argmax(vector vec){return max_element(vec.begin(), vec.end()) - vec.begin();} template inline void chmax(T &a, T b){a = max(a, b);} template inline void chmin(T &a, T b){a = min(a, b);} inline int toInt(string &s){int res = 0; for(char a : s) res = 10 * res + (a - '0'); return res;} inline int toInt(const string s){int res = 0; for(char a : s) res = 10 * res + (a - '0'); return res;} inline long long int toLong(string &s){lli res = 0; for(char a : s) res = 10 * res + (a - '0'); return res;} inline long long int toLong(const string s){lli res = 0; for(char a : s) res = 10 * res + (a - '0'); return res;} template inline std::string toString(T n){ if(n == 0) return "0"; std::string res = ""; if(n < 0){n = -n;while(n != 0){res += (char)(n % 10 + '0'); n /= 10;} std::reverse(res.begin(), res.end()); return '-' + res;} while(n != 0){res += (char)(n % 10 + '0'); n /= 10;} std::reverse(res.begin(), res.end()); return res; } // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ constexpr int MAX_SIZE = 2000 * 2000; // x^2 + y^2 + z^2 - w^2 = D // XY[i] := x^2 + y^2 = iとなる(x, y)の組の数 // ZW[i] := z^2 - w^2 = iとなる(z, w) (z ≥ w)の数 // then, ∑ XY[i]ZW[j] : i + j = D (i ≥ 2, j ≥ 0) => 2 ≤ i ≤ D // ∑ XY[i]ZW[j] : i - j = D (i ≥ 2, j ≥ 0) => D ≤ i Vint XY(2 * MAX_SIZE + 1, 0), ZW(MAX_SIZE + 1, 0); int main(void){ lli ans = 0; int n, d; cin >> n >> d; const int limit = min(2 * n * n, n * n + d); FOReq(x, 1, n) FOReq(y, 1, n) XY.at(x * x + y * y)++; FOReq(z, 1, n) FOReq(w, z, n) ZW.at((w-z)*(w+z))++; for(int i = 2; i < d; i++) ans += XY.at(i) * ZW.at(d-i); for(int i = d; i <= limit; i++) ans += XY.at(i) * ZW.at(i-d); printf("%lld\n", ans); return 0; }