#include <bits/stdc++.h>
#include "game.h"
using namespace std;
#pragma GCC optimize("Os")
int const R = 1 << 30, C = 1 << 30;
// ^ really good programming language
struct NodeX
{
int xChildren, yRoot;
};
struct NodeY
{
int yLeft, yRight;
long long g;
};
NodeX *root;
int allocNode(size_t s) { return (int)((char *)calloc(1, s) - (char *)root); }
char *getPtr(int offset) { return ((char *)root + offset); }
long long calculateY(int Q, int V, NodeY *z, int A, int B)
{
if (B < Q || A > V)
return 0;
if (Q <= A && B <= V)
return z->g;
long long g = 0;
if (z->yLeft)
g = gcd(g, calculateY(Q, V, (NodeY *)getPtr(z->yLeft), A, (A + B) / 2));
if (z->yRight)
g = gcd(g, calculateY(Q, V, (NodeY *)getPtr(z->yRight), (A + B) / 2 + 1, B));
return g;
}
long long calculateX(int P, int Q, int U, int V, NodeX *z, int A, int B)
{
if (B < P || A > U)
return 0;
if (P <= A && B <= U)
return z->yRoot ? calculateY(Q, V, (NodeY *)getPtr(z->yRoot), 0, C - 1) : 0;
if (z->xChildren)
return gcd(calculateX(P, Q, U, V, (NodeX *)getPtr(z->xChildren), A, (A + B) / 2),
calculateX(P, Q, U, V, (NodeX *)getPtr(z->xChildren) + 1, (A + B) / 2 + 1, B));
return 0;
}
void updateY(int Q, long long K, NodeY *z, int A, int B)
{
if (A == B)
{
z->g = K;
return;
}
if (Q <= (A + B) / 2)
{
if (!z->yLeft)
z->yLeft = allocNode(sizeof(NodeY));
updateY(Q, K, (NodeY *)getPtr(z->yLeft), A, (A + B) / 2);
}
else
{
if (!z->yRight)
z->yRight = allocNode(sizeof(NodeY));
updateY(Q, K, (NodeY *)getPtr(z->yRight), (A + B) / 2 + 1, B);
}
z->g = gcd(z->yLeft ? ((NodeY *)getPtr(z->yLeft))->g : 0,
z->yRight ? (((NodeY *)getPtr(z->yRight))->g) : 0);
}
void updateX(int P, int Q, long long K, NodeX *z, int A, int B)
{
if (!z->yRoot)
z->yRoot = allocNode(sizeof(NodeY));
if (A == B)
{
updateY(Q, K, (NodeY *)getPtr(z->yRoot), 0, C - 1);
return;
}
if (!z->xChildren)
z->xChildren = allocNode(2 * sizeof(NodeX));
if (P <= (A + B) / 2)
updateX(P, Q, K, (NodeX *)getPtr(z->xChildren), A, (A + B) / 2);
else
updateX(P, Q, K, (NodeX *)getPtr(z->xChildren) + 1, (A + B) / 2 + 1, B);
long long g = 0;
if (((NodeX *)getPtr(z->xChildren))->yRoot)
g = gcd(g, calculateY(Q, Q, (NodeY *)getPtr(((NodeX *)getPtr(z->xChildren))->yRoot), 0, C - 1));
if ((((NodeX *)getPtr(z->xChildren)) + 1)->yRoot)
g = gcd(g, calculateY(Q, Q, (NodeY *)getPtr(((NodeX *)getPtr(z->xChildren) + 1)->yRoot), 0, C - 1));
updateY(Q, g, (NodeY *)getPtr(z->yRoot), 0, C - 1);
}
void init(int R, int C) { root = (NodeX *)calloc(1, sizeof *root); }
void update(int P, int Q, long long K)
{
updateX(P, Q, K, root, 0, R - 1);
}
long long calculate(int P, int Q, int U, int V)
{
return calculateX(P, Q, U, V, root, 0, R - 1);
}
