Description
Input
Output
Sample Input1:
1 2
3 3
Sample Input2:
2 5
4 5
6 7
Sample Output1:
1
Sample Output2:
0
7
Data Constraint
對於n個物體中選取m個物體,可以想對於第n個物體的選取方式只有選和不選,那麼可得
c(n,m)=c(n-1,m)+c(n-1,m-1)
看到這條式子,發現特別像楊輝三角,在統計n,m的範圍內有多少個mod k爲0即可。
var
a,s:array[0..5000,0..5000] of longint;
i,j,t,k,n,m:longint;
begin
readln(t,k);
a[1,1]:=1 mod k;
for i:=2 to 2100 do
for j:=1 to i do
a[i,j]:=(a[i-1,j-1]+a[i-1,j]) mod k;
for i:=1 to 2100 do
for j:=1 to 2100 do
begin
s[i,j]:=s[i-1,j]+s[i,j-1]-s[i-1,j-1];
if (a[i,j]=0)and(j<=i) then inc(s[i,j]);
end;
for i:=1 to t do
begin
readln(n,m);
writeln(s[n+1,m+1]);
end;
end.