This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
#define gc() (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin), (iS == iT ? EOF : *iS++)) : *iS++)
namespace IO {
const int SIZE = 1 << 23;
char ibuf[SIZE], *iS, *iT;
char obuf[SIZE], *oS = obuf, *oT = oS + SIZE - 1;
bool flush() {
fwrite(obuf, 1, oS - obuf, stdout);
oS = obuf;
return true;
}
#define gc() (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin), (iS == iT ? EOF : *iS++)) : *iS++)
#define pc(x) (*oS++ = x)
int read() {
int x = 0, f = 0;
char c = gc();
while (!isdigit(c)) f |= c == '-', c = gc();
while (isdigit(c)) x = 10 * x + c - '0', c = gc();
return f ? -x : x;
}
char qu[55]; int qlen;
template <class T> void print(T x) {
if (!x) pc('0');
if (x < 0) pc('-'), x = -x;
while (x) qu[++qlen] = x % 10 + '0', x /= 10;
while (qlen) pc(qu[qlen--]);
}
template <class T> void print(T x, char charset) {
print(x), pc(charset);
}
struct Flusher {
~Flusher() {
flush();
}
} flusher;
}
using namespace IO;
const int N=3e4+9;
const int oo=1e9+9;
typedef pair <int,int> ii;
typedef pair <int,ii> iii;
int can,n,m,a[N],p[N],f[N][176];
bool First[N],check[N][176];
vector <int> num[N];
priority_queue <iii,vector<iii>,greater<iii> > q;
void update(int x,int dist,int val)
{
if (f[x][dist]>val)
{
f[x][dist]=val;
q.push({val,{x,dist}});
}
if (num[x].size()==0||dist==0) return;
}
int solve()
{
if (p[1]>=can)
{
f[a[1]][0]=0;
q.push({0,{a[1],0}});
}
else
{
f[a[1]][p[1]]=0;
q.push({0,{a[1],p[1]}});
}
int val,x,dist;
while (!q.empty())
{
val=q.top().first;
x=q.top().second.first;
dist=q.top().second.second;
q.pop();
if (x==a[2]) return f[x][dist];
if (f[x][dist]!=val) continue;
if (!First[x])
{
First[x]=true;
for (int i=0;i<can;i++)
if (check[x][i]||i==0) update(x,i,val);
}
if (dist!=0)
{
if (x+dist<=n) update(x+dist,dist,f[x][dist]+1);
if (x-dist>=1) update(x-dist,dist,f[x][dist]+1);
}
for (int xnew:num[x])
{
int dem=0;
for (int i=x+p[xnew];i<=n;i+=p[xnew])
{
// cout<<i<<endl;
dem++;
update(i,0,val+dem);
}
dem=0;
for (int i=x-p[xnew];i>=1;i-=p[xnew])
{
dem++;
update(i,0,val+dem);
}
}
// break;
}
int res=oo;
for (int i=0;i<=can;i++)
res=min(res,f[a[2]][i]);
if (res==oo) res=-1;
return res;
}
signed main()
{
// ios::sync_with_stdio(false);
// cin.tie(0);
// freopen("test.inp","r",stdin);
// cin>>n>>m;
n=read();
m=read();
can=sqrt(n);
for (int i=0;i<=n;i++)
for (int j=0;j<=can;j++)
f[i][j]=oo;
for (int i=1;i<=m;i++)
{
a[i]=read();
p[i]=read();
a[i]++;
if (p[i]>=can) num[a[i]].push_back(i);
else check[a[i]][p[i]]=true;
}
cout<<solve();
return 0;
}
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