#include <math.h>
#include <stdlib.h>
#include <stdio.h>

static int n;

struct ciara
{
  double a, b, c;
};

static struct ciara *c;


void setciara(int now, int from, int to, int what, double kolko)
{
  int mid=(from+to)/2;
  
  if(from==to)
    c[now].b=kolko;
   else
  if(what<=mid)
  {
    setciara(2*now, from, mid, what, kolko);
    c[now].b=c[2*now].b+c[2*now+1].b;
  }
   else
  {
    setciara(2*now+1, mid+1, to, what, kolko);
    c[now].b=c[2*now].b+c[2*now+1].b;
  }
}


double ga(int now, int from, int to, int what)
{
  int mid=(from+to)/2;
  
  if(from==to)
    return c[now].c;
   else
  if(what<=mid)
    return ga(2*now, from, mid, what);
   else
    return ga(2*now+1, mid+1, to, what);
}


void update(int now, int from, int to, int what, double uhol)
{
  int mid=(from+to)/2;
  double a, b, cc, uh;
  
  if(from==to)
  {
    c[now].a=uhol-ga(1, 0, n-1, what-1);
    return;
  }
  
  if(what<=mid)
    update(2*now, from, mid, what, uhol);
   else
    update(2*now+1, mid+1, to, what, uhol);
  
   a=c[2*now].b;
   b=c[2*now+1].b*cos(c[2*now].c+c[2*now+1].a);
   cc=c[2*now+1].b*sin(c[2*now].c+c[2*now+1].a);
  
   uh=atan2(cc, a+b);
  
  c[now].a=c[2*now].a+uh;
  c[now].c=c[2*now].a+c[2*now].c+c[2*now+1].a+c[2*now+1].c-c[now].a;
  
  c[now].b=sqrt((a+b)*(a+b)+cc*cc);
}


int main()
{
  int cc;
  int blank=0;
  c=malloc(sizeof(struct ciara)*50000);
  memset(c, 0, sizeof(struct ciara)*50000);
  
  
  while(scanf("%d %d ", &n, &cc)==2)
  {
    int i;
    
    memset(c, 0, sizeof(struct ciara)*50000);
    for(i=0; i<n; i++)
    {
      int a;

      scanf("%d ", &a);
      setciara(1, 0, n-1, i, a);
    }

      if(blank++)
        printf("\n");
    
    
    for(i=0; i<cc; i++)
    {
      int a,b;
      
      scanf("%d %d ", &a, &b);
      
      update(1, 0, n-1, a, 4*acos(0.0)*(double)b/360.0);
      
      
      printf("%f %f\n", c[1].b*sin(c[1].a), c[1].b*cos(c[1].a));
    }
  }

  return 0;
}