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| #include<bits/stdc++.h>
using namespace std;
typedef long long ll;
int d[20], m = 0;
ll ans, l, r;
int now;
ll dp[14][109][109];
int xxx[169400], yyy[169400], zzz[169400], cnt;
ll DP(int i, int mod, int sum) {
if(dp[i][mod][sum] != -1) return dp[i][mod][sum];
if(sum>now) return xxx[++cnt] = i, yyy[cnt] = mod, zzz[cnt] = sum, dp[i][mod][sum]=0;
if(sum+(9*i)<now) return xxx[++cnt] = i, yyy[cnt] = mod, zzz[cnt] = sum, dp[i][mod][sum]=0;
if(!i) {
xxx[++cnt] = i, yyy[cnt] = mod, zzz[cnt] = sum;
if(sum == now && mod == 0) return dp[i][mod][sum] = 1;
else return dp[i][mod][sum] = 0;
}
dp[i][mod][sum] = 0;
for(register int dg = 0; dg <= 9; dg++) dp[i][mod][sum] += DP(i-1,(mod * 10 + dg) % now, sum + dg);
xxx[++cnt] = i, yyy[cnt] = mod, zzz[cnt] = sum;
return dp[i][mod][sum];
}
ll calc(ll x) {
m = 0;
while(x) {
d[m++] = x%10; x /= 10;
}
memset(dp, -1, sizeof(dp));
ll ret = 0;
for(register int xx = 1; xx <= 9*m; xx++) {
now = xx;
cnt = 0;
ll ans = 0;
for(register int i = m-1; i >= 1; i--)
for(register int j = 1; j <= 9; j++)
ans += DP(i-1, j-j/now*now, j);
int pre1 = 0, pre2 = 0;
for(register int i = m-1; i >= 0; i--) {
for(register int j = (i == m - 1) ? 1 : 0; j <= d[i] - 1; j++)
ans += DP(i, (pre1 * 10 + j) - (pre1 * 10 + j)/now*now, (pre2 + j));
pre1 = (pre1 * 10 + d[i]);
pre1 -= pre1 / now * now;
pre2 += d[i];
}
for(int i = 1; i <= cnt; i++)
dp[xxx[i]][yyy[i]][zzz[i]] = -1;
ret += ans;
}
return ret;
}
int main() {
int t; scanf("%d", &t);
int cas = 0;
while(t--) {
scanf("%lld", &r);
printf("Case %d: %lld\n", ++cas, calc(r+1));
}
return 0;
}
|